Introduction to Finite and Infinite Dimensional Lie Super algebras

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

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  • Author : Neelacanta Sthanumoorthy
  • Publisher : Academic Press
  • Pages : 512 pages
  • ISBN : 012804683X
  • Rating : 4/5 from 21 reviews
CLICK HERE TO GET THIS BOOKIntroduction to Finite and Infinite Dimensional Lie Super algebras

Introduction to Finite and Infinite Dimensional Lie (Super)algebras

Introduction to Finite and Infinite Dimensional Lie (Super)algebras
  • Author : Neelacanta Sthanumoorthy
  • Publisher : Academic Press
  • Release : 26 April 2016
GET THIS BOOKIntroduction to Finite and Infinite Dimensional Lie (Super)algebras

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

Infinite-dimensional Lie Algebras

Infinite-dimensional Lie Algebras
  • Author : Minoru Wakimoto
  • Publisher : American Mathematical Soc.
  • Release : 17 April 2021
GET THIS BOOKInfinite-dimensional Lie Algebras

This volume begins with an introduction to the structure of finite-dimensional simple Lie algebras, including the representation of ${\widehat {\mathfrak {sl}}}(2, {\mathbb C})$, 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

Lectures on Infinite-Dimensional Lie Algebra

Lectures on Infinite-Dimensional Lie Algebra
  • Author : Minoru Wakimoto
  • Publisher : World Scientific
  • Release : 26 October 2001
GET THIS BOOKLectures on Infinite-Dimensional Lie Algebra

The representation theory of affine Lie algebras has been developed in close connection with various areas of mathematics and mathematical physics in the last two decades. There are three excellent books on it, written by Victor G Kac. This book begins with a survey and review of the material treated in Kac's books. In particular, modular invariance and conformal invariance are explained in more detail. The book then goes further, dealing with some of the recent topics involving the representation

Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras

Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras
  • Author : Victor G. Kac,Ashok K. Raina,Natasha Rozhkovskaya
  • Publisher : World Scientific
  • Release : 17 April 2021
GET THIS BOOKBombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras

The second edition of this book incorporates, as its first part, the largely unchanged text of the first edition, while its second part is the collection of lectures on vertex algebras, delivered by Professor Kac at the TIFR in January 2003. The basic idea of these lectures was to demonstrate how the key notions of the theory of vertex algebras--such as quantum fields, their normal ordered product and lambda-bracket, energy-momentum field and conformal weight, untwisted and twisted representations--simplify and clarify the

Infinite Dimensional Lie Superalgebras

Infinite Dimensional Lie Superalgebras
  • Author : Yuri Bahturin,Alexander V. Mikhalev,Viktor M. Petrogradsky,Mikhail V. Zaicev
  • Publisher : Walter de Gruyter
  • Release : 01 January 1992
GET THIS BOOKInfinite Dimensional Lie Superalgebras

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

Dualities and Representations of Lie Superalgebras

Dualities and Representations of Lie Superalgebras
  • Author : Shun-Jen Cheng,Weiqiang Wang
  • Publisher : American Mathematical Soc.
  • Release : 17 April 2021
GET THIS BOOKDualities and Representations of Lie Superalgebras

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.

Lie Algebras: Theory and Algorithms

Lie Algebras: Theory and Algorithms
  • Author : W.A. de Graaf
  • Publisher : Elsevier
  • Release : 04 February 2000
GET THIS BOOKLie Algebras: Theory and Algorithms

The aim of the present work is two-fold. Firstly it aims at a giving an account of many existing algorithms for calculating with finite-dimensional Lie algebras. Secondly, the book provides an introduction into the theory of finite-dimensional Lie algebras. These two subject areas are intimately related. First of all, the algorithmic perspective often invites a different approach to the theoretical material than the one taken in various other monographs (e.g., [42], [48], [77], [86]). Indeed, on various occasions the knowledge of certain algorithms

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

Ring Theory - Proceedings Of The Biennial Ohio State-denison Conference 1992
  • Author : Jain Surender K,Rizvi Syed Tariq
  • Publisher : World Scientific
  • Release : 30 September 1993
GET THIS BOOKRing Theory - Proceedings Of The Biennial Ohio State-denison Conference 1992

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

Automorphic Forms and Lie Superalgebras

Automorphic Forms and Lie Superalgebras
  • Author : Urmie Ray
  • Publisher : Springer Science & Business Media
  • Release : 06 March 2007
GET THIS BOOKAutomorphic Forms and Lie Superalgebras

This book provides the reader with the tools to understand the ongoing classification and construction project of Lie superalgebras. It presents the material in as simple terms as possible. Coverage specifically details Borcherds-Kac-Moody superalgebras. The book examines the link between the above class of Lie superalgebras and automorphic form and explains their construction from lattice vertex algebras. It also includes all necessary background information.

Lie Superalgebras and Enveloping Algebras

Lie Superalgebras and Enveloping Algebras
  • Author : Ian Malcolm Musson
  • Publisher : American Mathematical Soc.
  • Release : 04 April 2012
GET THIS BOOKLie Superalgebras and Enveloping Algebras

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

Notes on Lie Algebras

Notes on Lie Algebras
  • Author : Hans Samelson
  • Publisher : Springer Science & Business Media
  • Release : 06 December 2012
GET THIS BOOKNotes on Lie Algebras

(Cartan sub Lie algebra, roots, Weyl group, Dynkin diagram, . . . ) and the classification, as found by Killing and Cartan (the list of all semisimple Lie algebras consists of (1) the special- linear ones, i. e. all matrices (of any fixed dimension) with trace 0, (2) the orthogonal ones, i. e. all skewsymmetric ma trices (of any fixed dimension), (3) the symplectic ones, i. e. all matrices M (of any fixed even dimension) that satisfy M J = - J MT with a certain non-degenerate skewsymmetric matrix

Quantum Theoretic Machines

Quantum Theoretic Machines
  • Author : A. Stern
  • Publisher : Elsevier
  • Release : 08 December 2000
GET THIS BOOKQuantum Theoretic Machines

Making Sense of Inner Sense 'Terra cognita' is terra incognita. It is difficult to find someone not taken abackand fascinated by the incomprehensible but indisputable fact: there are material systems which are aware of themselves. Consciousness is self-cognizing code. During homo sapiens's relentness and often frustrated search for self-understanding various theories of consciousness have been and continue to be proposed. However, it remains unclear whether and at what level the problems of consciousness and intelligent thought can be resolved. Science's