Developments And Trends In Infinite Dimensional Lie Theory

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Developments and Trends in Infinite-Dimensional Lie Theory

Author : Karl-Hermann Neeb
Publisher : Springer Science & Business Media
ISBN 13 : 0817647414
Total Pages : 492 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Developments and Trends in Infinite-Dimensional Lie Theory by : Karl-Hermann Neeb

Download or read book Developments and Trends in Infinite-Dimensional Lie Theory written by Karl-Hermann Neeb and published by Springer Science & Business Media. This book was released on 2010-10-17 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts: infinite-dimensional Lie (super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups. Contributors: B. Allison, D. Beltiţă, W. Bertram, J. Faulkner, Ph. Gille, H. Glöckner, K.-H. Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf.

Developments and Trends in Infinite-dimensional Lie Theory: Geometry of infinite-dimensional lie (transformation) groups

Author :
Publisher :
ISBN 13 : 9781282973633
Total Pages : 492 pages
Book Rating : 4.9/5 (736 download)

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Book Synopsis Developments and Trends in Infinite-dimensional Lie Theory: Geometry of infinite-dimensional lie (transformation) groups by :

Download or read book Developments and Trends in Infinite-dimensional Lie Theory: Geometry of infinite-dimensional lie (transformation) groups written by and published by . This book was released on 2011 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts: infinite-dimensional Lie (super- )algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups. Part (A) is mainly concerned with the structure and representation theory of infinite-dimensional Lie algebras and contains articles on the structure of direct-limit Lie algebras, extended affine Lie algebras and loop algebras, as well as representations of loop algebras and Kac-Moody superalgebras. The articles in Part (B) examine connections between infinite-dimensional Lie theory and geometry. The topics range from infinite-dimensional groups acting on fiber bundles, corresponding characteristic classes and gerbes, to Jordan-theoretic geometries and new results on direct-limit groups. The analytic representation theory of infinite-dimensional Lie groups is still very much underdeveloped. The articles in Part (C) develop new, promising methods based on heat kernels, multiplicity freeness, Banach-Lie-Poisson spaces, and infinite-dimensional generalizations of reductive Lie groups. Contributors: B. Allison, D. Beltiţă, W. Bertram, J. Faulkner, Ph. Gille, H. Glöckner, K.-H. Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf.

Developments and Retrospectives in Lie Theory

Author : Geoffrey Mason
Publisher : Springer
ISBN 13 : 3319098047
Total Pages : 397 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Developments and Retrospectives in Lie Theory by : Geoffrey Mason

Download or read book Developments and Retrospectives in Lie Theory written by Geoffrey Mason and published by Springer. This book was released on 2014-10-31 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Lie Theory Workshop, founded by Joe Wolf (UC, Berkeley), has been running for over two decades. These workshops have been sponsored by the NSF, noting the talks have been seminal in describing new perspectives in the field covering broad areas of current research. At the beginning, the top universities in California and Utah hosted the meetings which continue to run on a quarterly basis. Experts in representation theory/Lie theory from various parts of the US, Europe, Asia (China, Japan, Singapore, Russia), Canada, and South and Central America were routinely invited to give talks at these meetings. Nowadays, the workshops are also hosted at universities in Louisiana, Virginia, and Oklahoma. The contributors to this volume have all participated in these Lie theory workshops and include in this volume expository articles which cover representation theory from the algebraic, geometric, analytic, and topological perspectives with also important connections to math physics. These survey articles, review and update the prominent seminal series of workshops in representation/Lie theory mentioned-above, and reflects the widespread influence of those workshops in such areas as harmonic analysis, representation theory, differential geometry, algebraic geometry, number theory, and mathematical physics. Many of the contributors have had prominent roles in both the classical and modern developments of Lie theory and its applications.

Smooth Homotopy of Infinite-Dimensional $C^{infty }$-Manifolds

$Download Smooth Homotopy of Infinite-Dimensional $C^{infty }$-Manifolds PDF Online Free$

Author : Hiroshi Kihara
Publisher : American Mathematical Society
ISBN 13 : 1470465426
Total Pages : 144 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Smooth Homotopy of Infinite-Dimensional $C^{infty }$-Manifolds by : Hiroshi Kihara

Download or read book Smooth Homotopy of Infinite-Dimensional $C^{infty }$-Manifolds written by Hiroshi Kihara and published by American Mathematical Society. This book was released on 2023-09-27 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Perspectives in Lie Theory

Author : Filippo Callegaro
Publisher : Springer
ISBN 13 : 3319589717
Total Pages : 461 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Perspectives in Lie Theory by : Filippo Callegaro

Download or read book Perspectives in Lie Theory written by Filippo Callegaro and published by Springer. This book was released on 2017-12-07 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie theory is a mathematical framework for encoding the concept of symmetries of a problem, and was the central theme of an INdAM intensive research period at the Centro de Giorgi in Pisa, Italy, in the academic year 2014-2015. This book gathers the key outcomes of this period, addressing topics such as: structure and representation theory of vertex algebras, Lie algebras and superalgebras, as well as hyperplane arrangements with different approaches, ranging from geometry and topology to combinatorics.

Quantum Affine Algebras, Extended Affine Lie Algebras, and Their Applications

Author : Yun Gao
Publisher : American Mathematical Soc.
ISBN 13 : 0821845071
Total Pages : 314 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Quantum Affine Algebras, Extended Affine Lie Algebras, and Their Applications by : Yun Gao

Download or read book Quantum Affine Algebras, Extended Affine Lie Algebras, and Their Applications written by Yun Gao and published by American Mathematical Soc.. This book was released on 2010 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference on Quantum Affine Algebras, Extended Affine Lie Algebras, and Applications, which was held at the Banff International Research Station, Banff, Canada, from March 2-7, 2008. Many of the papers include new results on different aspects of quantum affine algebras, extended affine Lie algebras, and their applications in other areas of mathematics and physics. Any reader interested in learning about the recent developments in quantum affine algebras and extended affine Lie algebras will benefit from this book.

Infinite-dimensional Analysis: Operators In Hilbert Space; Stochastic Calculus Via Representations, And Duality Theory

Author : Palle Jorgensen
Publisher : World Scientific
ISBN 13 : 9811225796
Total Pages : 253 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Infinite-dimensional Analysis: Operators In Hilbert Space; Stochastic Calculus Via Representations, And Duality Theory by : Palle Jorgensen

Download or read book Infinite-dimensional Analysis: Operators In Hilbert Space; Stochastic Calculus Via Representations, And Duality Theory written by Palle Jorgensen and published by World Scientific. This book was released on 2021-01-15 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to make available to beginning graduate students, and to others, some core areas of analysis which serve as prerequisites for new developments in pure and applied areas. We begin with a presentation (Chapters 1 and 2) of a selection of topics from the theory of operators in Hilbert space, algebras of operators, and their corresponding spectral theory. This is a systematic presentation of interrelated topics from infinite-dimensional and non-commutative analysis; again, with view to applications. Chapter 3 covers a study of representations of the canonical commutation relations (CCRs); with emphasis on the requirements of infinite-dimensional calculus of variations, often referred to as Ito and Malliavin calculus, Chapters 4-6. This further connects to key areas in quantum physics.

Advances in Lie Superalgebras

Author : Maria Gorelik
Publisher : Springer Science & Business
ISBN 13 : 3319029525
Total Pages : 280 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Advances in Lie Superalgebras by : Maria Gorelik

Download or read book Advances in Lie Superalgebras written by Maria Gorelik and published by Springer Science & Business. This book was released on 2014-04-28 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume is the outcome of the conference "Lie superalgebras," which was held at the Istituto Nazionale di Alta Matematica, in 2012. The conference gathered many specialists in the subject, and the talks held provided comprehensive insights into the newest trends in research on Lie superalgebras (and related topics like vertex algebras, representation theory and supergeometry). The book contains contributions of many leading esperts in the field and provides a complete account of the newest trends in research on Lie Superalgebras.

Geometric Analysis and Integral Geometry

Author : Eric Todd Quinto
Publisher : American Mathematical Soc.
ISBN 13 : 0821887386
Total Pages : 299 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Geometric Analysis and Integral Geometry by : Eric Todd Quinto

Download or read book Geometric Analysis and Integral Geometry written by Eric Todd Quinto and published by American Mathematical Soc.. This book was released on 2013 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an historical overview of several decades in integral geometry and geometric analysis as well as recent advances in these fields and closely related areas. It contains several articles focusing on the mathematical work of Sigurdur Helgason, including an overview of his research by Gestur Olafsson and Robert Stanton.

Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory

Author : Stephen Berman
Publisher : American Mathematical Soc.
ISBN 13 : 0821827162
Total Pages : 346 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory by : Stephen Berman

Download or read book Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory written by Stephen Berman and published by American Mathematical Soc.. This book was released on 2002 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Because of its many applications to mathematics and mathematical physics, the representation theory of infinite-dimensional Lie and quantized enveloping algebras comprises an important area of current research. This volume includes articles from the proceedings of an international conference, ``Infinite-Dimensional Lie Theory and Conformal Field Theory'', held at the University of Virginia. Many of the contributors to the volume are prominent researchers in the field. Thisconference provided an opportunity for mathematicians and physicists to interact in an active research area of mutual interest. The talks focused on recent developments in the representation theory of affine, quantum affine, and extended affine Lie algebras and Lie superalgebras. They also highlightedapplications to conformal field theory, integrable and disordered systems. Some of the articles are expository and accessible to a broad readership of mathematicians and physicists interested in this area; others are research articles that are appropriate for more advanced readers.

Dualities and Representations of Lie Superalgebras

Author : Shun-Jen Cheng
Publisher : American Mathematical Soc.
ISBN 13 : 0821891189
Total Pages : 323 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Dualities and Representations of Lie Superalgebras by : Shun-Jen Cheng

Download or read book Dualities and Representations of Lie Superalgebras written by Shun-Jen Cheng and published by American Mathematical Soc.. This book was released on 2012 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a systematic account of the structure and representation theory of finite-dimensional complex Lie superalgebras of classical type and serves as a good introduction to representation theory of Lie superalgebras. Several folklore results are rigorously proved (and occasionally corrected in detail), sometimes with new proofs. Three important dualities are presented in the book, with the unifying theme of determining irreducible characters of Lie superalgebras. In order of increasing sophistication, they are Schur duality, Howe duality, and super duality. The combinatorics of symmetric functions is developed as needed in connections to Harish-Chandra homomorphism as well as irreducible characters for Lie superalgebras. Schur-Sergeev duality for the queer Lie superalgebra is presented from scratch with complete detail. Howe duality for Lie superalgebras is presented in book form for the first time. Super duality is a new approach developed in the past few years toward understanding the Bernstein-Gelfand-Gelfand category of modules for classical Lie superalgebras. Super duality relates the representation theory of classical Lie superalgebras directly to the representation theory of classical Lie algebras and thus gives a solution to the irreducible character problem of Lie superalgebras via the Kazhdan-Lusztig polynomials of classical Lie algebras.

Representations and Nilpotent Orbits of Lie Algebraic Systems

Author : Maria Gorelik
Publisher : Springer Nature
ISBN 13 : 3030235319
Total Pages : 553 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Representations and Nilpotent Orbits of Lie Algebraic Systems by : Maria Gorelik

Download or read book Representations and Nilpotent Orbits of Lie Algebraic Systems written by Maria Gorelik and published by Springer Nature. This book was released on 2019-10-18 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, a celebration of Anthony Joseph’s fundamental influence on classical and quantized representation theory, explores a wide array of current topics in Lie theory by experts in the area. The chapters are based on the 2017 sister conferences titled “Algebraic Modes of Representations,” the first of which was held from July 16-18 at the Weizmann Institute of Science and the second from July 19-23 at the University of Haifa. The chapters in this volume cover a range of topics, including: Primitive ideals Invariant theory Geometry of Lie group actions Quantum affine algebras Yangians Categorification Vertex algebras This volume is addressed to mathematicians who specialize in representation theory and Lie theory, and who wish to learn more about this fascinating subject.

Representation Theory and Mathematical Physics

Author : Jeffrey Adams
Publisher : American Mathematical Soc.
ISBN 13 : 0821852469
Total Pages : 404 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Representation Theory and Mathematical Physics by : Jeffrey Adams

Download or read book Representation Theory and Mathematical Physics written by Jeffrey Adams and published by American Mathematical Soc.. This book was released on 2011-11-07 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference on Representation Theory and Mathematical Physics, in honor of Gregg Zuckerman's 60th birthday, held October 24-27, 2009, at Yale University. Lie groups and their representations play a fundamental role in mathematics, in particular because of connections to geometry, topology, number theory, physics, combinatorics, and many other areas. Representation theory is one of the cornerstones of the Langlands program in number theory, dating to the 1970s. Zuckerman's work on derived functors, the translation principle, and coherent continuation lie at the heart of the modern theory of representations of Lie groups. One of the major unsolved problems in representation theory is that of the unitary dual. The fact that there is, in principle, a finite algorithm for computing the unitary dual relies heavily on Zuckerman's work. In recent years there has been a fruitful interplay between mathematics and physics, in geometric representation theory, string theory, and other areas. New developments on chiral algebras, representation theory of affine Kac-Moody algebras, and the geometric Langlands correspondence are some of the focal points of this volume. Recent developments in the geometric Langlands program point to exciting connections between certain automorphic representations and dual fibrations in geometric mirror symmetry.

Representation Theory, Mathematical Physics, and Integrable Systems

Author : Anton Alekseev
Publisher : Springer Nature
ISBN 13 : 3030781488
Total Pages : 652 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Representation Theory, Mathematical Physics, and Integrable Systems by : Anton Alekseev

Download or read book Representation Theory, Mathematical Physics, and Integrable Systems written by Anton Alekseev and published by Springer Nature. This book was released on 2022-02-05 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the course of his distinguished career, Nicolai Reshetikhin has made a number of groundbreaking contributions in several fields, including representation theory, integrable systems, and topology. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and physicists and pay tribute to his many significant and lasting achievements. Covering the latest developments at the interface of noncommutative algebra, differential and algebraic geometry, and perspectives arising from physics, this volume explores topics such as the development of new and powerful knot invariants, new perspectives on enumerative geometry and string theory, and the introduction of cluster algebra and categorification techniques into a broad range of areas. Chapters will also cover novel applications of representation theory to random matrix theory, exactly solvable models in statistical mechanics, and integrable hierarchies. The recent progress in the mathematical and physicals aspects of deformation quantization and tensor categories is also addressed. Representation Theory, Mathematical Physics, and Integrable Systems will be of interest to a wide audience of mathematicians interested in these areas and the connections between them, ranging from graduate students to junior, mid-career, and senior researchers.

Highlights in Lie Algebraic Methods

Author : Anthony Joseph
Publisher : Springer Science & Business Media
ISBN 13 : 0817682740
Total Pages : 236 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Highlights in Lie Algebraic Methods by : Anthony Joseph

Download or read book Highlights in Lie Algebraic Methods written by Anthony Joseph and published by Springer Science & Business Media. This book was released on 2011-10-20 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of expository and research articles that highlight the various Lie algebraic methods used in mathematical research today. Key topics discussed include spherical varieties, Littelmann Paths and Kac–Moody Lie algebras, modular representations, primitive ideals, representation theory of Artin algebras and quivers, Kac–Moody superalgebras, categories of Harish–Chandra modules, cohomological methods, and cluster algebras.

Direct and Projective Limits of Geometric Banach Structures.

Author : Patrick Cabau
Publisher : CRC Press
ISBN 13 : 1000966011
Total Pages : 1516 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Direct and Projective Limits of Geometric Banach Structures. by : Patrick Cabau

Download or read book Direct and Projective Limits of Geometric Banach Structures. written by Patrick Cabau and published by CRC Press. This book was released on 2023-10-06 with total page 1516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes in detail the basic context of the Banach setting and the most important Lie structures found in finite dimension. The authors expose these concepts in the convenient framework which is a common context for projective and direct limits of Banach structures. The book presents sufficient conditions under which these structures exist by passing to such limits. In fact, such limits appear naturally in many mathematical and physical domains. Many examples in various fields illustrate the different concepts introduced. Many geometric structures, existing in the Banach setting, are "stable" by passing to projective and direct limits with adequate conditions. The convenient framework is used as a common context for such types of limits. The contents of this book can be considered as an introduction to differential geometry in infinite dimension but also a way for new research topics. This book allows the intended audience to understand the extension to the Banach framework of various topics in finite dimensional differential geometry and, moreover, the properties preserved by passing to projective and direct limits of such structures as a tool in different fields of research.

Algebra, Geometry, and Physics in the 21st Century

Author : Denis Auroux
Publisher : Birkhäuser
ISBN 13 : 3319599399
Total Pages : 364 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Algebra, Geometry, and Physics in the 21st Century by : Denis Auroux

Download or read book Algebra, Geometry, and Physics in the 21st Century written by Denis Auroux and published by Birkhäuser. This book was released on 2017-07-27 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a tribute to Maxim Kontsevich, one of the most original and influential mathematicians of our time. Maxim’s vision has inspired major developments in many areas of mathematics, ranging all the way from probability theory to motives over finite fields, and has brought forth a paradigm shift at the interface of modern geometry and mathematical physics. Many of his papers have opened completely new directions of research and led to the solutions of many classical problems. This book collects papers by leading experts currently engaged in research on topics close to Maxim’s heart. Contributors: S. Donaldson A. Goncharov D. Kaledin M. Kapranov A. Kapustin L. Katzarkov A. Noll P. Pandit S. Pimenov J. Ren P. Seidel C. Simpson Y. Soibelman R. Thorngren