Lie Methods In Deformation Theory

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Lie Methods in Deformation Theory

Author : Marco Manetti
Publisher : Springer
ISBN 13 : 9789811911842
Total Pages : 0 pages
Book Rating : 4.9/5 (118 download)

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Book Synopsis Lie Methods in Deformation Theory by : Marco Manetti

Download or read book Lie Methods in Deformation Theory written by Marco Manetti and published by Springer. This book was released on 2022-09-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book furnishes a comprehensive treatment of differential graded Lie algebras, L-infinity algebras, and their use in deformation theory. We believe it is the first textbook devoted to this subject, although the first chapters are also covered in other sources with a different perspective. Deformation theory is an important subject in algebra and algebraic geometry, with an origin that dates back to Kodaira, Spencer, Kuranishi, Gerstenhaber, and Grothendieck. In the last 30 years, a new approach, based on ideas from rational homotopy theory, has made it possible not only to solve long-standing open problems, but also to clarify the general theory and to relate apparently different features. This approach works over a field of characteristic 0, and the central role is played by the notions of differential graded Lie algebra, L-infinity algebra, and Maurer–Cartan equations. The book is written keeping in mind graduate students with a basic knowledge of homological algebra and complex algebraic geometry as utilized, for instance, in the book by K. Kodaira, Complex Manifolds and Deformation of Complex Structures. Although the main applications in this book concern deformation theory of complex manifolds, vector bundles, and holomorphic maps, the underlying algebraic theory also applies to a wider class of deformation problems, and it is a prerequisite for anyone interested in derived deformation theory. Researchers in algebra, algebraic geometry, algebraic topology, deformation theory, and noncommutative geometry are the major targets for the book.

Lie Methods in Deformation Theory

Author : Marco Manetti
Publisher : Springer Nature
ISBN 13 : 9811911851
Total Pages : 576 pages
Book Rating : 4.8/5 (119 download)

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Book Synopsis Lie Methods in Deformation Theory by : Marco Manetti

Download or read book Lie Methods in Deformation Theory written by Marco Manetti and published by Springer Nature. This book was released on 2022-08-01 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book furnishes a comprehensive treatment of differential graded Lie algebras, L-infinity algebras, and their use in deformation theory. We believe it is the first textbook devoted to this subject, although the first chapters are also covered in other sources with a different perspective. Deformation theory is an important subject in algebra and algebraic geometry, with an origin that dates back to Kodaira, Spencer, Kuranishi, Gerstenhaber, and Grothendieck. In the last 30 years, a new approach, based on ideas from rational homotopy theory, has made it possible not only to solve long-standing open problems, but also to clarify the general theory and to relate apparently different features. This approach works over a field of characteristic 0, and the central role is played by the notions of differential graded Lie algebra, L-infinity algebra, and Maurer–Cartan equations. The book is written keeping in mind graduate students with a basic knowledge of homological algebra and complex algebraic geometry as utilized, for instance, in the book by K. Kodaira, Complex Manifolds and Deformation of Complex Structures. Although the main applications in this book concern deformation theory of complex manifolds, vector bundles, and holomorphic maps, the underlying algebraic theory also applies to a wider class of deformation problems, and it is a prerequisite for anyone interested in derived deformation theory. Researchers in algebra, algebraic geometry, algebraic topology, deformation theory, and noncommutative geometry are the major targets for the book.

Maurer–Cartan Methods in Deformation Theory

Author : Vladimir Dotsenko
Publisher : Cambridge University Press
ISBN 13 : 1108967027
Total Pages : 188 pages
Book Rating : 4.1/5 (89 download)

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Book Synopsis Maurer–Cartan Methods in Deformation Theory by : Vladimir Dotsenko

Download or read book Maurer–Cartan Methods in Deformation Theory written by Vladimir Dotsenko and published by Cambridge University Press. This book was released on 2023-08-31 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering an exceptional range of topics, this text provides a unique overview of the Maurer—Cartan methods in algebra, geometry, topology, and mathematical physics. It offers a new conceptual treatment of the twisting procedure, guiding the reader through various versions with the help of plentiful motivating examples for graduate students as well as researchers. Topics covered include a novel approach to the twisting procedure for operads leading to Kontsevich graph homology and a description of the twisting procedure for (homotopy) associative algebras or (homotopy) Lie algebras using the biggest deformation gauge group ever considered. The book concludes with concise surveys of recent applications in areas including higher category theory and deformation theory.

Maurer–Cartan Methods in Deformation Theory

Author : Vladimir Dotsenko
Publisher : Cambridge University Press
ISBN 13 : 1108965644
Total Pages : 187 pages
Book Rating : 4.1/5 (89 download)

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Book Synopsis Maurer–Cartan Methods in Deformation Theory by : Vladimir Dotsenko

Download or read book Maurer–Cartan Methods in Deformation Theory written by Vladimir Dotsenko and published by Cambridge University Press. This book was released on 2023-08-31 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering an exceptional range of topics, this text provides a unique overview of the Maurer-Cartan methods in algebra, geometry, topology, and mathematical physics. It offers a new conceptual treatment of the twisting procedure, guiding the reader through various versions with the help of plentiful motivating examples for graduate students as well as researchers. Topics covered include a novel approach to the twisting procedure for operads leading to Kontsevich graph homology and a description of the twisting procedure for (homotopy) associative algebras or (homotopy) Lie algebras using the biggest deformation gauge group ever considered. The book concludes with concise surveys of recent applications in areas including higher category theory and deformation theory.

Deformation Theory of Discontinuous Groups

Author : Ali Baklouti
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110765306
Total Pages : 498 pages
Book Rating : 4.1/5 (17 download)

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Book Synopsis Deformation Theory of Discontinuous Groups by : Ali Baklouti

Download or read book Deformation Theory of Discontinuous Groups written by Ali Baklouti and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-07-05 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the latest developments of the theory of discontinuous groups acting on homogenous spaces, from basic concepts to a comprehensive exposition. It develops the newest approaches and methods in the deformation theory of topological modules and unitary representations and focuses on the geometry of discontinuous groups of solvable Lie groups and their compact extensions. It also presents proofs of recent results, computes fundamental examples, and serves as an introduction and reference for students and experienced researchers in Lie theory, discontinuous groups, and deformation (and moduli) spaces.

Déformation, quantification, théorie de Lie

Author : Alberto S. Cattaneo
Publisher : Societe Mathematique de France
ISBN 13 :
Total Pages : 210 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Déformation, quantification, théorie de Lie by : Alberto S. Cattaneo

Download or read book Déformation, quantification, théorie de Lie written by Alberto S. Cattaneo and published by Societe Mathematique de France. This book was released on 2005 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1997, M. Kontsevich proved that every Poisson manifold admits a formal quantization, canonical up to equivalence. In doing so he solved a longstanding problem in mathematical physics. Through his proof and his interpretation of a later proof given by Tamarkin, he also opened up new research avenues in Lie theory, quantum group theory, deformation theory and the study of operads ... and uncovered fascinating links of these topics with number theory, knot theory and the theory of motives. Without doubt, his work on deformation quantization will continue to influence these fields for many years to come. In the three parts of this volume, we will 1) present the main results of Kontsevich's 1997 preprint and sketch his interpretation of Tamarkin's approach, 2) show the relevance of Kontsevich's theorem for Lie theory and 3) explain the idea from topological string theory which inspired Kontsevich's proof. An appendix is devoted to the geometry of configuration spaces.

Generalized Lie Theory in Mathematics, Physics and Beyond

Author : Sergei D. Silvestrov
Publisher : Springer Science & Business Media
ISBN 13 : 3540853324
Total Pages : 308 pages
Book Rating : 4.5/5 (48 download)

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Book Synopsis Generalized Lie Theory in Mathematics, Physics and Beyond by : Sergei D. Silvestrov

Download or read book Generalized Lie Theory in Mathematics, Physics and Beyond written by Sergei D. Silvestrov and published by Springer Science & Business Media. This book was released on 2008-11-18 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the cutting edge of the fundamental role of generalizations of Lie theory and related non-commutative and non-associative structures in mathematics and physics.

Deformation Theory of Discontinuous Groups

Author : Ali Baklouti
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311076539X
Total Pages : 379 pages
Book Rating : 4.1/5 (17 download)

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Book Synopsis Deformation Theory of Discontinuous Groups by : Ali Baklouti

Download or read book Deformation Theory of Discontinuous Groups written by Ali Baklouti and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-07-05 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the latest developments of the theory of discontinuous groups acting on homogenous spaces, from basic concepts to a comprehensive exposition. It develops the newest approaches and methods in the deformation theory of topological modules and unitary representations and focuses on the geometry of discontinuous groups of solvable Lie groups and their compact extensions. It also presents proofs of recent results, computes fundamental examples, and serves as an introduction and reference for students and experienced researchers in Lie theory, discontinuous groups, and deformation (and moduli) spaces.

Algebraic Topology. Aarhus 1982

Author : I. Madsen
Publisher : Springer
ISBN 13 : 354038782X
Total Pages : 674 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Algebraic Topology. Aarhus 1982 by : I. Madsen

Download or read book Algebraic Topology. Aarhus 1982 written by I. Madsen and published by Springer. This book was released on 2006-11-14 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Deformation Theory of Algebras and Structures and Applications

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
ISBN 13 : 9400930577
Total Pages : 1024 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Deformation Theory of Algebras and Structures and Applications by : Michiel Hazewinkel

Download or read book Deformation Theory of Algebras and Structures and Applications written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 1024 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a result of a meeting which took place in June 1986 at 'll Ciocco" in Italy entitled 'Deformation theory of algebras and structures and applications'. It appears somewhat later than is perhaps desirable for a volume resulting from a summer school. In return it contains a good many results which were not yet available at the time of the meeting. In particular it is now abundantly clear that the Deformation theory of algebras is indeed central to the whole philosophy of deformations/perturbations/stability. This is one of the main results of the 254 page paper below (practically a book in itself) by Gerstenhaber and Shack entitled "Algebraic cohomology and defor mation theory". Two of the main philosphical-methodological pillars on which deformation theory rests are the fol lowing • (Pure) To study a highly complicated object, it is fruitful to study the ways in which it can arise as a limit of a family of simpler objects: "the unraveling of complicated structures" . • (Applied) If a mathematical model is to be applied to the real world there will usually be such things as coefficients which are imperfectly known. Thus it is important to know how the behaviour of a model changes as it is perturbed (deformed).

Geometric and Topological Methods for Quantum Field Theory

Author : Sylvie Paycha
Publisher : American Mathematical Soc.
ISBN 13 : 0821840622
Total Pages : 272 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Geometric and Topological Methods for Quantum Field Theory by : Sylvie Paycha

Download or read book Geometric and Topological Methods for Quantum Field Theory written by Sylvie Paycha and published by American Mathematical Soc.. This book was released on 2007 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, based on lectures and short communications at a summer school in Villa de Leyva, Colombia (July 2005), offers an introduction to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. It is aimed at graduate students in physics or mathematics who might want insight in the following topics (covered in five survey lectures): Anomalies and noncommutative geometry, Deformation quantisation and Poisson algebras, Topological quantum field theory and orbifolds. These lectures are followed by nine articles on various topics at the borderline of mathematics and physics ranging from quasicrystals to invariant instantons through black holes, and involving a number of mathematical tools borrowed from geometry, algebra and analysis.

Group Theoretical Methods in Physics

Author : G.S Pogosyan
Publisher : CRC Press
ISBN 13 : 9780750310086
Total Pages : 630 pages
Book Rating : 4.3/5 (1 download)

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Book Synopsis Group Theoretical Methods in Physics by : G.S Pogosyan

Download or read book Group Theoretical Methods in Physics written by G.S Pogosyan and published by CRC Press. This book was released on 2005-05-01 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetry is permeating our understanding of nature: Group theoretical methods of intrinsic interest to mathematics have expanded their applications from physics to chemistry and biology. The ICGTMP Colloquia maintain the communication among the many branches into which this endeavor has bloomed. Lie group and representation theory, special functions, foundations of quantum mechanics, and elementary particle, nuclear, atomic, and molecular physics are among the traditional subjects. More recent areas include supersymmetry, superstrings and quantum gravity, integrability, nonlinear systems and quantum chaos, semigroups, time asymmetry and resonances, condensed matter, and statistical physics. Topics such as linear and nonlinear optics, quantum computing, discrete systems, and signal analysis have only in the last few years become part of the group theorists' turf. In Group Theoretical Methods in Physics, readers will find both review contributions that distill the state of the art in a broad field, and articles pointed to specific problems, in many cases, preceding their formal publication in the journal literature.

Naive Lie Theory

Author : John Stillwell
Publisher : Springer Science & Business Media
ISBN 13 : 038778215X
Total Pages : 230 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Naive Lie Theory by : John Stillwell

Download or read book Naive Lie Theory written by John Stillwell and published by Springer Science & Business Media. This book was released on 2008-12-15 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this new textbook, acclaimed author John Stillwell presents a lucid introduction to Lie theory suitable for junior and senior level undergraduates. In order to achieve this, he focuses on the so-called "classical groups'' that capture the symmetries of real, complex, and quaternion spaces. These symmetry groups may be represented by matrices, which allows them to be studied by elementary methods from calculus and linear algebra. This naive approach to Lie theory is originally due to von Neumann, and it is now possible to streamline it by using standard results of undergraduate mathematics. To compensate for the limitations of the naive approach, end of chapter discussions introduce important results beyond those proved in the book, as part of an informal sketch of Lie theory and its history. John Stillwell is Professor of Mathematics at the University of San Francisco. He is the author of several highly regarded books published by Springer, including The Four Pillars of Geometry (2005), Elements of Number Theory (2003), Mathematics and Its History (Second Edition, 2002), Numbers and Geometry (1998) and Elements of Algebra (1994).

Lie Theory and Its Applications in Physics

Author : Vladimir Dobrev
Publisher : Springer Nature
ISBN 13 : 9811577757
Total Pages : 552 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Lie Theory and Its Applications in Physics by : Vladimir Dobrev

Download or read book Lie Theory and Its Applications in Physics written by Vladimir Dobrev and published by Springer Nature. This book was released on 2020-10-15 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents modern trends in the area of symmetries and their applications based on contributions to the workshop "Lie Theory and Its Applications in Physics" held near Varna (Bulgaria) in June 2019. Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a large interdisciplinary and interrelated field. The topics covered in this volume from the workshop represent the most modern trends in the field : Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Polylogarithms, and Supersymmetry. They also include Supersymmetric Calogero-type models, Quantum Groups, Deformations, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, and Exceptional Quantum Algebra for the standard model of particle physics This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.

Character Map In Non-abelian Cohomology, The: Twisted, Differential, And Generalized

Author : Domenico Fiorenza
Publisher : World Scientific
ISBN 13 : 9811276714
Total Pages : 248 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Character Map In Non-abelian Cohomology, The: Twisted, Differential, And Generalized by : Domenico Fiorenza

Download or read book Character Map In Non-abelian Cohomology, The: Twisted, Differential, And Generalized written by Domenico Fiorenza and published by World Scientific. This book was released on 2023-08-11 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a novel development of fundamental and fascinating aspects of algebraic topology and mathematical physics: 'extra-ordinary' and further generalized cohomology theories enhanced to 'twisted' and differential-geometric form, with focus on, firstly, their rational approximation by generalized Chern character maps, and then, the resulting charge quantization laws in higher n-form gauge field theories appearing in string theory and the classification of topological quantum materials.Although crucial for understanding famously elusive effects in strongly interacting physics, the relevant higher non-abelian cohomology theory ('higher gerbes') has had an esoteric reputation and remains underdeveloped.Devoted to this end, this book's theme is that various generalized cohomology theories are best viewed through their classifying spaces (or moduli stacks) — not necessarily infinite-loop spaces — from which perspective the character map is really an incarnation of the fundamental theorem of rational homotopy theory, thereby not only uniformly subsuming the classical Chern character and a multitude of scattered variants that have been proposed, but now seamlessly applicable in the hitherto elusive generality of (twisted, differential, and) non-abelian cohomology.In laying out this result with plenty of examples, this book provides a modernized introduction and review of fundamental classical topics: 1. abstract homotopy theory via model categories; 2. generalized cohomology in its homotopical incarnation; 3. rational homotopy theory seen via homotopy Lie theory, whose fundamental theorem we recast as a (twisted) non-abelian de Rham theorem, which naturally induces the (twisted) non-abelian character map.

Lie Algebras and Applications

Author : Francesco Iachello Sloane
Publisher : Springer
ISBN 13 : 9783662444955
Total Pages : 272 pages
Book Rating : 4.4/5 (449 download)

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Book Synopsis Lie Algebras and Applications by : Francesco Iachello Sloane

Download or read book Lie Algebras and Applications written by Francesco Iachello Sloane and published by Springer. This book was released on 2014-10-19 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This course-based primer provides an introduction to Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. In the first part, it concisely presents the basic concepts of Lie algebras, their representations and their invariants. The second part includes a description of how Lie algebras are used in practice in the treatment of bosonic and fermionic systems. Physical applications considered include rotations and vibrations of molecules (vibron model), collective modes in nuclei (interacting boson model), the atomic shell model, the nuclear shell model, and the quark model of hadrons. One of the key concepts in the application of Lie algebraic methods in physics, that of spectrum generating algebras and their associated dynamic symmetries, is also discussed. The book highlights a number of examples that help to illustrate the abstract algebraic definitions and includes a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators, and the dimensions of the representations of all classical Lie algebras. For this new edition, the text has been carefully revised and expanded; in particular, a new chapter has been added on the deformation and contraction of Lie algebras. From the reviews of the first edition: "Iachello has written a pedagogical and straightforward presentation of Lie algebras [...]. It is a great text to accompany a course on Lie algebras and their physical applications." (Marc de Montigny, Mathematical Reviews, Issue, 2007 i) "This book [...] written by one of the leading experts in the field [...] will certainly be of great use for students or specialists that want to refresh their knowledge on Lie algebras applied to physics. [...] An excellent reference for those interested in acquiring practical experience [...] and leaving the embarrassing theoretical presentations aside." (Rutwig Campoamor-Stursberg, Zentralblatt MATH, Vol. 1156, 2009)

Lie Algebras and Applications

Author : Francesco Iachello
Publisher : Springer
ISBN 13 : 3540362398
Total Pages : 208 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Lie Algebras and Applications by : Francesco Iachello

Download or read book Lie Algebras and Applications written by Francesco Iachello and published by Springer. This book was released on 2007-02-22 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, designed for advanced graduate students and post-graduate researchers, introduces Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. The book contains many examples that help to elucidate the abstract algebraic definitions. It provides a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators and the dimensions of the representations of all classical Lie algebras.