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The Generalised Jacobson Morosov Theorem
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Book Synopsis The Generalised Jacobson-Morosov Theorem by : Peter O'Sullivan
Download or read book The Generalised Jacobson-Morosov Theorem written by Peter O'Sullivan and published by American Mathematical Soc.. This book was released on 2010-08-06 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author considers homomorphisms $H \to K$ from an affine group scheme $H$ over a field $k$ of characteristic zero to a proreductive group $K$. Using a general categorical splitting theorem, Andre and Kahn proved that for every $H$ there exists such a homomorphism which is universal up to conjugacy. The author gives a purely group-theoretic proof of this result. The classical Jacobson-Morosov theorem is the particular case where $H$ is the additive group over $k$. As well as universal homomorphisms, the author considers more generally homomorphisms $H \to K$ which are minimal, in the sense that $H \to K$ factors through no proper proreductive subgroup of $K$. For fixed $H$, it is shown that the minimal $H \to K$ with $K$ reductive are parametrised by a scheme locally of finite type over $k$.
Book Synopsis Nilpotent Orbits In Semisimple Lie Algebra by : William.M. McGovern
Download or read book Nilpotent Orbits In Semisimple Lie Algebra written by William.M. McGovern and published by Routledge. This book was released on 2017-10-19 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through the 1990s, a circle of ideas emerged relating three very different kinds of objects associated to a complex semisimple Lie algebra: nilpotent orbits, representations of a Weyl group, and primitive ideals in an enveloping algebra. The principal aim of this book is to collect together the important results concerning the classification and properties of nilpotent orbits, beginning from the common ground of basic structure theory. The techniques used are elementary and in the toolkit of any graduate student interested in the harmonic analysis of representation theory of Lie groups. The book develops the Dynkin-Konstant and Bala-Carter classifications of complex nilpotent orbits, derives the Lusztig-Spaltenstein theory of induction of nilpotent orbits, discusses basic topological questions, and classifies real nilpotent orbits. The classical algebras are emphasized throughout; here the theory can be simplified by using the combinatorics of partitions and tableaux. The authors conclude with a survey of advanced topics related to the above circle of ideas. This book is the product of a two-quarter course taught at the University of Washington.
Book Synopsis Nilpotent Orbits In Semisimple Lie Algebra by : William.M. McGovern
Download or read book Nilpotent Orbits In Semisimple Lie Algebra written by William.M. McGovern and published by Routledge. This book was released on 2017-10-19 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through the 1990s, a circle of ideas emerged relating three very different kinds of objects associated to a complex semisimple Lie algebra: nilpotent orbits, representations of a Weyl group, and primitive ideals in an enveloping algebra. The principal aim of this book is to collect together the important results concerning the classification and properties of nilpotent orbits, beginning from the common ground of basic structure theory. The techniques used are elementary and in the toolkit of any graduate student interested in the harmonic analysis of representation theory of Lie groups. The book develops the Dynkin-Konstant and Bala-Carter classifications of complex nilpotent orbits, derives the Lusztig-Spaltenstein theory of induction of nilpotent orbits, discusses basic topological questions, and classifies real nilpotent orbits. The classical algebras are emphasized throughout; here the theory can be simplified by using the combinatorics of partitions and tableaux. The authors conclude with a survey of advanced topics related to the above circle of ideas. This book is the product of a two-quarter course taught at the University of Washington.
Book Synopsis Families of Automorphic Forms and the Trace Formula by : Werner Müller
Download or read book Families of Automorphic Forms and the Trace Formula written by Werner Müller and published by Springer. This book was released on 2016-09-20 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: Featuring the work of twenty-three internationally-recognized experts, this volume explores the trace formula, spectra of locally symmetric spaces, p-adic families, and other recent techniques from harmonic analysis and representation theory. Each peer-reviewed submission in this volume, based on the Simons Foundation symposium on families of automorphic forms and the trace formula held in Puerto Rico in January-February 2014, is the product of intensive research collaboration by the participants over the course of the seven-day workshop. The goal of each session in the symposium was to bring together researchers with diverse specialties in order to identify key difficulties as well as fruitful approaches being explored in the field. The respective themes were counting cohomological forms, p-adic trace formulas, Hecke fields, slopes of modular forms, and orbital integrals.
Book Synopsis Representation Theory and Algebraic Geometry by : Vladimir Baranovsky
Download or read book Representation Theory and Algebraic Geometry written by Vladimir Baranovsky and published by Springer Nature. This book was released on 2022-06-15 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: The chapters in this volume explore the influence of the Russian school on the development of algebraic geometry and representation theory, particularly the pioneering work of two of its illustrious members, Alexander Beilinson and Victor Ginzburg, in celebration of their 60th birthdays. Based on the work of speakers and invited participants at the conference “Interactions Between Representation Theory and Algebraic Geometry”, held at the University of Chicago, August 21-25, 2017, this volume illustrates the impact of their research and how it has shaped the development of various branches of mathematics through the use of D-modules, the affine Grassmannian, symplectic algebraic geometry, and other topics. All authors have been deeply influenced by their ideas and present here cutting-edge developments on modern topics. Chapters are organized around three distinct themes: Groups, algebras, categories, and representation theory D-modules and perverse sheaves Analogous varieties defined by quivers Representation Theory and Algebraic Geometry will be an ideal resource for researchers who work in the area, particularly those interested in exploring the impact of the Russian school.
Book Synopsis D-Modules, Perverse Sheaves, and Representation Theory by : Ryoshi Hotta
Download or read book D-Modules, Perverse Sheaves, and Representation Theory written by Ryoshi Hotta and published by Springer Science & Business Media. This book was released on 2007-11-07 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, analysis, differential equations, and representation theory. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors' essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics. To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, representation theory.
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).
Book Synopsis Geometric Representation Theory and Extended Affine Lie Algebras by : Erhard Neher
Download or read book Geometric Representation Theory and Extended Affine Lie Algebras written by Erhard Neher and published by American Mathematical Soc.. This book was released on 2011 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie theory has connections to many other disciplines such as geometry, number theory, mathematical physics, and algebraic combinatorics. The interaction between algebra, geometry and combinatorics has proven to be extremely powerful in shedding new light on each of these areas. This book presents the lectures given at the Fields Institute Summer School on Geometric Representation Theory and Extended Affine Lie Algebras held at the University of Ottawa in 2009. It provides a systematic account by experts of some of the exciting developments in Lie algebras and representation theory in the last two decades. It includes topics such as geometric realizations of irreducible representations in three different approaches, combinatorics and geometry of canonical and crystal bases, finite $W$-algebras arising as the quantization of the transversal slice to a nilpotent orbit, structure theory of extended affine Lie algebras, and representation theory of affine Lie algebras at level zero. This book will be of interest to mathematicians working in Lie algebras and to graduate students interested in learning the basic ideas of some very active research directions. The extensive references in the book will be helpful to guide non-experts to the original sources.
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. This book was released on 2015-01-26 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear PDE, special functions, and others. Furthermore, the necessary tools from functional analysis and number theory are included. This is a big interdisciplinary and interrelated field. Samples of these fresh trends are presented in this volume, based on contributions from the Workshop "Lie Theory and Its Applications in Physics" held near Varna (Bulgaria) in June 2013. This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists and researchers in the field of Lie Theory.
Book Synopsis Geometric Aspects of the Trace Formula by : Werner Müller
Download or read book Geometric Aspects of the Trace Formula written by Werner Müller and published by Springer. This book was released on 2018-10-11 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second of three volumes devoted to the study of the trace formula, these proceedings focus on automorphic representations of higher rank groups. Based on research presented at the 2016 Simons Symposium on Geometric Aspects of the Trace Formula that took place in Schloss Elmau, Germany, the volume contains both original research articles and articles that synthesize current knowledge and future directions in the field. The articles discuss topics such as the classification problem of representations of reductive groups, the structure of Langlands and Arthur packets, interactions with geometric representation theory, and conjectures on the global automorphic spectrum. Suitable for both graduate students and researchers, this volume presents the latest research in the field. Readers of the first volume Families of Automorphic Forms and the Trace Formula will find this a natural continuation of the study of the trace formula.
Book Synopsis Handbook of Geometry and Topology of Singularities I by : José Luis Cisneros Molina
Download or read book Handbook of Geometry and Topology of Singularities I written by José Luis Cisneros Molina and published by Springer Nature. This book was released on 2020-10-24 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of ten articles which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject. This is the first volume in a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.
Book Synopsis Algebras, Representations and Applications by : V. Futorny
Download or read book Algebras, Representations and Applications written by V. Futorny and published by American Mathematical Soc.. This book was released on 2009 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains contributions from the conference on "Algebras, Representations and Applications" (Maresias, Brazil, August 26-September 1, 2007), in honor of Ivan Shestakov's 60th birthday. The collection of papers presented here is of great interest to graduate students and researchers working in the theory of Lie and Jordan algebras and superalgebras and their representations, Hopf algebras, Poisson algebras, Quantum Groups, Group Rings and other topics.
Book Synopsis Affine, Vertex and W-algebras by : Dražen Adamović
Download or read book Affine, Vertex and W-algebras written by Dražen Adamović and published by Springer Nature. This book was released on 2019-11-28 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on recent developments in the theory of vertex algebras, with particular emphasis on affine vertex algebras, affine W-algebras, and W-algebras appearing in physical theories such as logarithmic conformal field theory. It is widely accepted in the mathematical community that the best way to study the representation theory of affine Kac–Moody algebras is by investigating the representation theory of the associated affine vertex and W-algebras. In this volume, this general idea can be seen at work from several points of view. Most relevant state of the art topics are covered, including fusion, relationships with finite dimensional Lie theory, permutation orbifolds, higher Zhu algebras, connections with combinatorics, and mathematical physics. The volume is based on the INdAM Workshop Affine, Vertex and W-algebras, held in Rome from 11 to 15 December 2017. It will be of interest to all researchers in the field.
Author :Camille Laurent-Gengoux Publisher :Springer Science & Business Media ISBN 13 :3642310907 Total Pages :470 pages Book Rating :4.6/5 (423 download)
Book Synopsis Poisson Structures by : Camille Laurent-Gengoux
Download or read book Poisson Structures written by Camille Laurent-Gengoux and published by Springer Science & Business Media. This book was released on 2012-08-27 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Poisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory. In each one of these contexts, it turns out that the Poisson structure is not a theoretical artifact, but a key element which, unsolicited, comes along with the problem that is investigated, and its delicate properties are decisive for the solution to the problem in nearly all cases. Poisson Structures is the first book that offers a comprehensive introduction to the theory, as well as an overview of the different aspects of Poisson structures. The first part covers solid foundations, the central part consists of a detailed exposition of the different known types of Poisson structures and of the (usually mathematical) contexts in which they appear, and the final part is devoted to the two main applications of Poisson structures (integrable systems and deformation quantization). The clear structure of the book makes it adequate for readers who come across Poisson structures in their research or for graduate students or advanced researchers who are interested in an introduction to the many facets and applications of Poisson structures.
Book Synopsis Algebraic Quotients. Torus Actions and Cohomology. The Adjoint Representation and the Adjoint Action by : A. Bialynicki-Birula
Download or read book Algebraic Quotients. Torus Actions and Cohomology. The Adjoint Representation and the Adjoint Action written by A. Bialynicki-Birula and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume of the new subseries "Invariant Theory and Algebraic Transformation Groups". The aim of the survey by A. Bialynicki-Birula is to present the main trends and achievements of research in the theory of quotients by actions of algebraic groups. This theory contains geometric invariant theory with various applications to problems of moduli theory. The contribution by J. Carrell treats the subject of torus actions on algebraic varieties, giving a detailed exposition of many of the cohomological results one obtains from having a torus action with fixed points. Many examples, such as toric varieties and flag varieties, are discussed in detail. W.M. McGovern studies the actions of a semisimple Lie or algebraic group on its Lie algebra via the adjoint action and on itself via conjugation. His contribution focuses primarily on nilpotent orbits that have found the widest application to representation theory in the last thirty-five years.
Download or read book Algebra IX written by A.I. Kostrikin and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first contribution by Carter covers the theory of finite groups of Lie type, an important field of current mathematical research. In the second part, Platonov and Yanchevskii survey the structure of finite-dimensional division algebras, including an account of reduced K-theory.
Book Synopsis Perverse Sheaves and Applications to Representation Theory by : Pramod N. Achar
Download or read book Perverse Sheaves and Applications to Representation Theory written by Pramod N. Achar and published by American Mathematical Soc.. This book was released on 2021-09-27 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its inception around 1980, the theory of perverse sheaves has been a vital tool of fundamental importance in geometric representation theory. This book, which aims to make this theory accessible to students and researchers, is divided into two parts. The first six chapters give a comprehensive account of constructible and perverse sheaves on complex algebraic varieties, including such topics as Artin's vanishing theorem, smooth descent, and the nearby cycles functor. This part of the book also has a chapter on the equivariant derived category, and brief surveys of side topics including étale and ℓ-adic sheaves, D-modules, and algebraic stacks. The last four chapters of the book show how to put this machinery to work in the context of selected topics in geometric representation theory: Kazhdan-Lusztig theory; Springer theory; the geometric Satake equivalence; and canonical bases for quantum groups. Recent developments such as the p-canonical basis are also discussed. The book has more than 250 exercises, many of which focus on explicit calculations with concrete examples. It also features a 4-page “Quick Reference” that summarizes the most commonly used facts for computations, similar to a table of integrals in a calculus textbook.
