Dualities And Representations Of Lie Superalgebras
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Dualities And Representations Of Lie Superalgebras
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Author : Shun-Jen Cheng
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Dualities And Representations Of Lie Superalgebras written by Shun-Jen Cheng and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
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.
Schur Weyl Dualities For Lie Superalgebras And Lie Color Algebras
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Author : Dongho Moon
language : en
Publisher:
Release Date : 1998
Schur Weyl Dualities For Lie Superalgebras And Lie Color Algebras written by Dongho Moon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
Lie Superalgebras And Enveloping Algebras
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Author : Ian Malcolm Musson
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-04-04
Lie Superalgebras And Enveloping Algebras written by Ian Malcolm Musson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-04 with Mathematics categories.
Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. This book develops the theory of Lie superalgebras, their enveloping algebras, and their representations. The book begins with five chapters on the basic properties of Lie superalgebras, including explicit constructions for all the classical simple Lie superalgebras. Borel subalgebras, which are more subtle in this setting, are studied and described. Contragredient Lie superalgebras are introduced, allowing a unified approach to several results, in particular to the existence of an invariant bilinear form on $\mathfrak{g}$. The enveloping algebra of a finite dimensional Lie superalgebra is studied as an extension of the enveloping algebra of the even part of the superalgebra. By developing general methods for studying such extensions, important information on the algebraic structure is obtained, particularly with regard to primitive ideals. Fundamental results, such as the Poincare-Birkhoff-Witt Theorem, are established. Representations of Lie superalgebras provide valuable tools for understanding the algebras themselves, as well as being of primary interest in applications to other fields. Two important classes of representations are the Verma modules and the finite dimensional representations. The fundamental results here include the Jantzen filtration, the Harish-Chandra homomorphism, the Sapovalov determinant, supersymmetric polynomials, and Schur-Weyl duality. Using these tools, the center can be explicitly described in the general linear and orthosymplectic cases. In an effort to make the presentation as self-contained as possible, some background material is included on Lie theory, ring theory, Hopf algebras, and combinatorics.
Lie Theory
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Author : Jean-Philippe Anker
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lie Theory written by Jean-Philippe Anker and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
* First of three independent, self-contained volumes under the general title, "Lie Theory," featuring original results and survey work from renowned mathematicians. * Contains J. C. Jantzen's "Nilpotent Orbits in Representation Theory," and K.-H. Neeb's "Infinite Dimensional Groups and their Representations." * Comprehensive treatments of the relevant geometry of orbits in Lie algebras, or their duals, and the correspondence to representations. * Should benefit graduate students and researchers in mathematics and mathematical physics.
Lie Groups Lie Algebras And Their Representations
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Author : V.S. Varadarajan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Lie Groups Lie Algebras And Their Representations written by V.S. Varadarajan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
This book has grown out of a set of lecture notes I had prepared for a course on Lie groups in 1966. When I lectured again on the subject in 1972, I revised the notes substantially. It is the revised version that is now appearing in book form. The theory of Lie groups plays a fundamental role in many areas of mathematics. There are a number of books on the subject currently available -most notably those of Chevalley, Jacobson, and Bourbaki-which present various aspects of the theory in great depth. However, 1 feei there is a need for a single book in English which develops both the algebraic and analytic aspects of the theory and which goes into the representation theory of semi simple Lie groups and Lie algebras in detail. This book is an attempt to fiii this need. It is my hope that this book will introduce the aspiring graduate student as well as the nonspecialist mathematician to the fundamental themes of the subject. I have made no attempt to discuss infinite-dimensional representations. This is a very active field, and a proper treatment of it would require another volume (if not more) of this size. However, the reader who wants to take up this theory will find that this book prepares him reasonably well for that task.
Dictionary On Lie Algebras And Superalgebras
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Author : Luc Frappat
language : en
Publisher:
Release Date : 2000
Dictionary On Lie Algebras And Superalgebras written by Luc Frappat and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This book is a detailed reference on Lie algebras and Lie superalgebras presented in the form of a dictionary. It is intended to be useful to mathematical and theoretical physicists, from the level of the graduate student upwards. The Dictionary will serve as the reference of choice for practitioners and students alike. Key Features: * Compiles and presents material currently scattered throughout numerous textbooks and specialist journal articles * Dictionary format provides an easy to use reference on the essential topics concerning Lie algebras and Lie superalgebras * Covers the structure of Lie algebras and Lie superalgebras and their finite dimensional representation theory * Includes numerous tables of the properties of individual Lie algebras and Lie superalgebras
Lie Algebras And Their Representations
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Author : Seok-Jin Kang
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Lie Algebras And Their Representations written by Seok-Jin Kang and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
Over the past 30 years, exciting developments in diverse areas of the theory of Lie algebras and their representations have been observed. The symposium covered topics such as Lie algebras and combinatorics, crystal bases for quantum groups, quantum groups and solvable lattice models, and modular and infinite-dimensional Lie algebras. In this volume, readers will find several excellent expository articles and research papers containing many significant new results in this area.
The Theory Of Lie Superalgebras
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Author : M. Scheunert
language : en
Publisher: Springer
Release Date : 2006-11-15
The Theory Of Lie Superalgebras written by M. Scheunert and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Lie Algebras Lie Superalgebras Vertex Algebras And Related Topics
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Author : Kailash C. Misra
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-06-28
Lie Algebras Lie Superalgebras Vertex Algebras And Related Topics written by Kailash C. Misra and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-28 with Group theory and generalizations categories.
This book contains the proceedings of the 2012–2014 Southeastern Lie Theory Workshop Series held at North Carolina State University in April 2012, at College of Charleston in December 2012, at Louisiana State University in May 2013, and at University of Georgia in May 2014. Some of the articles by experts in the field survey recent developments while others include new results in representations of Lie algebras, and quantum groups, vertex (operator) algebras and Lie superalgebras.
Recent Developments In Lie Algebras Groups And Representation Theory
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Author : Kailash C. Misra
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Recent Developments In Lie Algebras Groups And Representation Theory written by Kailash C. Misra and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
This book contains the proceedings of the 2009-2011 Southeastern Lie Theory Workshop Series, held October 9-11, 2009 at North Carolina State University, May 22-24, 2010, at the University of Georgia, and June 1-4, 2011 at the University of Virginia. Some of the articles, written by experts in the field, survey recent developments while others include new results in Lie algebras, quantum groups, finite groups, and algebraic groups.