Introduction to Finite and Infinite Dimensional Lie  Super algebras Book

Introduction to Finite and Infinite Dimensional Lie Super algebras


  • Author : Neelacanta Sthanumoorthy
  • Publisher : Academic Press
  • Release Date : 2016-04-26
  • Genre: Mathematics
  • Pages : 512
  • ISBN 10 : 9780128046838

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Introduction to Finite and Infinite Dimensional Lie Super algebras Excerpt :

Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. Introduction to Finite and Infinite Dimensional Lie Algebras and Superalgebras introduces the theory of Lie superalgebras, their algebras, and their representations. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semi-simple Lie algebras. While discussing all classes of finite and infinite dimensional Lie algebras and Lie superalgebras in terms of their different classes of root systems, the book focuses on Kac-Moody algebras. With numerous exercises and worked examples, it is ideal for graduate courses on Lie groups and Lie algebras. Discusses the fundamental structure and all root relationships of Lie algebras and Lie superalgebras and their finite and infinite dimensional representation theory Closely describes BKM Lie superalgebras, their different classes of imaginary root systems, their complete classifications, root-supermultiplicities, and related combinatorial identities Includes numerous tables of the properties of individual Lie algebras and Lie superalgebras Focuses on Kac-Moody algebras

Introduction to Finite and Infinite Dimensional Lie  Super Algebras Book

Introduction to Finite and Infinite Dimensional Lie Super Algebras


  • Author : Sthanumoorthy Neelacanta
  • Publisher : Academic Press
  • Release Date : 2016-04-01
  • Genre: Uncategoriezed
  • Pages : 492
  • ISBN 10 : 0128046759

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Introduction to Finite and Infinite Dimensional Lie Super Algebras Excerpt :

Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. Introduction to Finite and Infinite Dimensional Lie Algebras and Superalgebras introduces the theory of Lie superalgebras, their algebras, and their representations. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semi-simple Lie algebras. While discussing all classes of finite and infinite dimensional Lie algebras and Lie superalgebras in terms of their different classes of root systems, the book focuses on Kac-Moody algebras. With numerous exercises and worked examples, it is ideal for graduate courses on Lie groups and Lie algebras. Discusses the fundamental structure and all root relationships of Lie algebras and Lie superalgebras and their finite and infinite dimensional representation theory Closely describes BKM Lie superalgebras, their different classes of imaginary root systems, their complete classifications, root-supermultiplicities, and related combinatorial identities Includes numerous tables of the properties of individual Lie algebras and Lie superalgebras Focuses on Kac-Moody algebras

Infinite dimensional Lie Algebras Book

Infinite dimensional Lie Algebras


  • Author : Minoru Wakimoto
  • Publisher : American Mathematical Soc.
  • Release Date : 2001
  • Genre: Mathematics
  • Pages : 332
  • ISBN 10 : 0821826549

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Infinite dimensional Lie Algebras Excerpt :

This volume begins with an introduction to the structure of finite-dimensional simple Lie algebras, including the representation of ...... root systems, the Cartan matrix, and a Dynkin diagram of a finite-dimensional simple Lie algebra. Continuing on, the main subjects of the book are the structure (real and imaginary root systems) of and the character formula for Kac-Moody superalgebras, which is explained in a very general setting. Only elementary linear algebra and group theory are assumed. Also covered is modular property and asymptotic behavior of integrable characters of affine Lie algebras. The exposition is self-contained and includes examples. The book can be used in a graduate-level course on the topic.

Infinite Dimensional Lie Algebras Book

Infinite Dimensional Lie Algebras


  • Author : Victor G. Kac
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-11-11
  • Genre: Mathematics
  • Pages : 252
  • ISBN 10 : 9781475713824

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Infinite Dimensional Lie Algebras Excerpt :

Infinite Dimensional Lie Superalgebras Book

Infinite Dimensional Lie Superalgebras


  • Author : Yuri Bahturin
  • Publisher : Walter de Gruyter
  • Release Date : 1992-01-01
  • Genre: Mathematics
  • Pages : 260
  • ISBN 10 : 9783110851205

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Infinite Dimensional Lie Superalgebras Excerpt :

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

Advances in Lie Superalgebras Book

Advances in Lie Superalgebras


  • Author : Maria Gorelik
  • Publisher : Springer Science & Business
  • Release Date : 2014-04-28
  • Genre: Mathematics
  • Pages : 280
  • ISBN 10 : 9783319029528

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Advances in Lie Superalgebras 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.

Ring Theory   Proceedings Of The Biennial Ohio State denison Conference 1992 Book

Ring Theory Proceedings Of The Biennial Ohio State denison Conference 1992


  • Author : Jain Surender K
  • Publisher : World Scientific
  • Release Date : 1993-09-30
  • Genre: Uncategoriezed
  • Pages : 392
  • ISBN 10 : 9789814553124

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Ring Theory Proceedings Of The Biennial Ohio State denison Conference 1992 Excerpt :

This invaluable book deals with the many-electron theory of the solid state. Mastery of the material in it will equip the reader for research in areas such as high-temperature superconductors and the fractional quantum Hall effect. The whole book has been designed to provide the diligent reader with a wide variety of approaches to many-electron theory.The level of the book is suitable for research workers and higher-degree students in a number of disciplines, embracing theoretical physics, materials science and solid-state chemistry. It should be useful not only to theorists in these areas but also to experimental scientists who desire to orient their programmes to address outstanding questions raised by many-body theory.

Groups  Rings  Lie and Hopf Algebras Book

Groups Rings Lie and Hopf Algebras


  • Author : Y. Bahturin
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-12-01
  • Genre: Mathematics
  • Pages : 241
  • ISBN 10 : 9781461302353

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Groups Rings Lie and Hopf Algebras Excerpt :

The volume is almost entirely composed of the research and expository papers by the participants of the International Workshop "Groups, Rings, Lie and Hopf Algebras", which was held at the Memorial University of Newfoundland, St. John's, NF, Canada. All four areas from the title of the workshop are covered. In addition, some chapters touch upon the topics, which belong to two or more areas at the same time. Audience: The readership targeted includes researchers, graduate and senior undergraduate students in mathematics and its applications.

Supersymmetries and Infinite Dimensional Algebras Book

Supersymmetries and Infinite Dimensional Algebras


  • Author : N. H. March
  • Publisher : Academic Press
  • Release Date : 2013-10-22
  • Genre: Mathematics
  • Pages : 628
  • ISBN 10 : 9781483288376

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Supersymmetries and Infinite Dimensional Algebras Excerpt :

Recent devopments, particularly in high-energy physics, have projected group theory and symmetry consideration into a central position in theoretical physics. These developments have taken physicists increasingly deeper into the fascinating world of pure mathematics. This work presents important mathematical developments of the last fifteen years in a form that is easy to comprehend and appreciate.

Lie Groups and Invariant Theory Book

Lie Groups and Invariant Theory


  • Author : Ėrnest Borisovich Vinberg
  • Publisher : American Mathematical Soc.
  • Release Date : 2005
  • Genre: Mathematics
  • Pages : 284
  • ISBN 10 : 0821837338

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Lie Groups and Invariant Theory Excerpt :

This volume, devoted to the 70th birthday of A. L. Onishchik, contains a collection of articles by participants in the Moscow Seminar on Lie Groups and Invariant Theory headed by E. B. Vinberg and A. L. Onishchik. The book is suitable for graduate students and researchers interested in Lie groups and related topics.

Dualities and Representations of Lie Superalgebras Book

Dualities and Representations of Lie Superalgebras


  • Author : Shun-Jen Cheng
  • Publisher : American Mathematical Soc.
  • Release Date : 2012
  • Genre: Mathematics
  • Pages : 302
  • ISBN 10 : 9780821891186

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Dualities and Representations of Lie Superalgebras 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.

The Geometry of Infinite Dimensional Groups Book

The Geometry of Infinite Dimensional Groups


  • Author : Boris Khesin
  • Publisher : Springer Science & Business Media
  • Release Date : 2008-09-28
  • Genre: Mathematics
  • Pages : 304
  • ISBN 10 : 9783540772637

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The Geometry of Infinite Dimensional Groups Excerpt :

This monograph gives an overview of various classes of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrable systems, gauge theory, and complex geometry. The text includes many exercises and open questions.

Introduction to Vertex Operator Superalgebras and Their Modules Book

Introduction to Vertex Operator Superalgebras and Their Modules


  • Author : Xiaoping Xu
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-03-09
  • Genre: Mathematics
  • Pages : 360
  • ISBN 10 : 9789401590976

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Introduction to Vertex Operator Superalgebras and Their Modules Excerpt :

This book presents a systematic study on the structures of vertex operator superalgebras and their modules. Related theories of self-dual codes and lattices are included, as well as recent achievements on classifications of certain simple vertex operator superalgebras and their irreducible twisted modules, constructions of simple vertex operator superalgebras from graded associative algebras and their anti-involutions, self-dual codes and lattices. Audience: This book is of interest to researchers and graduate students in mathematics and mathematical physics.

Developments and Trends in Infinite Dimensional Lie Theory Book

Developments and Trends in Infinite Dimensional Lie Theory


  • Author : Karl-Hermann Neeb
  • Publisher : Springer Science & Business Media
  • Release Date : 2010-10-17
  • Genre: Mathematics
  • Pages : 492
  • ISBN 10 : 9780817647414

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Developments and Trends in Infinite Dimensional Lie Theory 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.

Quantum Lie Theory Book

Quantum Lie Theory


  • Author : Vladislav Kharchenko
  • Publisher : Springer
  • Release Date : 2015-12-24
  • Genre: Mathematics
  • Pages : 302
  • ISBN 10 : 9783319227047

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Quantum Lie Theory Excerpt :

This is an introduction to the mathematics behind the phrase “quantum Lie algebra”. The numerous attempts over the last 15-20 years to define a quantum Lie algebra as an elegant algebraic object with a binary “quantum” Lie bracket have not been widely accepted. In this book, an alternative approach is developed that includes multivariable operations. Among the problems discussed are the following: a PBW-type theorem; quantum deformations of Kac--Moody algebras; generic and symmetric quantum Lie operations; the Nichols algebras; the Gurevich--Manin Lie algebras; and Shestakov--Umirbaev operations for the Lie theory of nonassociative products. Opening with an introduction for beginners and continuing as a textbook for graduate students in physics and mathematics, the book can also be used as a reference by more advanced readers. With the exception of the introductory chapter, the content of this monograph has not previously appeared in book form.