# Download Ebook Free Introduction To Finite And Infinite Dimensional Lie (Super)algebras

## Introduction to Finite and Infinite Dimensional Lie (Super)Algebras

Publisher : Academic Press

Release Date : 2016-04-01

Category :

Total pages :492

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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

Publisher : Academic Press

Release Date : 2016-04-26

Category : Mathematics

Total pages :512

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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

Publisher : American Mathematical Soc.

Release Date : 2001

Category : Mathematics

Total pages :304

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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 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.

## Supersymmetries and Infinite-Dimensional Algebras

Publisher : Academic Press

Release Date : 2013-10-22

Category : Mathematics

Total pages :628

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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.

## Journal of Group Theory in Physics

Publisher : Unknown

Release Date : 1995

Category : Group theory

Total pages :129

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## JMSJ

Publisher : Unknown

Release Date : 2005

Category : Mathematics

Total pages :129

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## Mathematical Reviews

Publisher : Unknown

Release Date : 2008

Category : Mathematics

Total pages :129

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## Recent Developments in Infinite-dimensional Lie Algebras and Conformal Field Theory

Publisher : American Mathematical Soc.

Release Date : 2002

Category : Mathematics

Total pages :334

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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.

## Advances in Theoretical and Mathematical Physics

Publisher : Unknown

Release Date : 2001

Category : Mathematical physics

Total pages :129

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## Seminari di geometria

Publisher : Unknown

Release Date : 2004

Category : Geometry

Total pages :129

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## Quantum Stochastic Calculus and Representations of Lie Superalgebras

Publisher : Springer

Release Date : 2006-11-14

Category : Mathematics

Total pages :148

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This book describes the representations of Lie superalgebras that are yielded by a graded version of Hudson-Parthasarathy quantum stochastic calculus. Quantum stochastic calculus and grading theory are given concise introductions, extending readership to mathematicians and physicists with a basic knowledge of algebra and infinite-dimensional Hilbert spaces. The develpment of an explicit formula for the chaotic expansion of a polynomial of quantum stochastic integrals is particularly interesting. The book aims to provide a self-contained exposition of what is known about Z_2-graded quantum stochastic calculus and to provide a framework for future research into this new and fertile area.

## Krichever–Novikov Type Algebras

Publisher : Walter de Gruyter GmbH & Co KG

Release Date : 2014-08-19

Category : Mathematics

Total pages :375

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Krichever and Novikov introduced certain classes of infinite dimensionalLie algebrasto extend the Virasoro algebra and its related algebras to Riemann surfaces of higher genus. The author of this book generalized and extended them toa more general setting needed by the applications. Examples of applications are Conformal Field Theory, Wess-Zumino-Novikov-Witten models, moduli space problems, integrable systems, Lax operator algebras, and deformation theory of Lie algebra. Furthermore they constitute an important class of infinite dimensional Lie algebras which due to their geometric origin are still manageable. This book gives an introduction for the newcomer to this exciting field of ongoing research in mathematics and will be a valuable source of reference for the experienced researcher. Beside the basic constructions and results also applications are presented.

## General Catalog -- University of California, Santa Cruz

Publisher : Unknown

Release Date : 2006

Category :

Total pages :129

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## Conformal Invariance and Applications to Statistical Mechanics

Publisher : World Scientific

Release Date : 1998-09-29

Category :

Total pages :994

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This volume contains Introductory Notes and major reprints on conformal field theory and its applications to 2-dimensional statistical mechanics of critical phenomena. The subject relates to many different areas in contemporary physics and mathematics, including string theory, integrable systems, representations of infinite Lie algebras and automorphic functions. Contents:General Principles:Infinite Conformal Symmetry in Two-dimensional Quantum Field Theory (A A Belavin et al.)Conformal Invariance and Surface Critical Behaviour (J Cardy)Mathematical Background:Contravariant Form for Infinite-dimensional Lie Algebras and Superalgebras (V Kac)Verma Modules over the Virasoro Algebra (B Feigin & D Fuks)Unitary Representations of the Virasoro and Super-Virasoro Algebras (P Goddard et al.)Critical Models and Computation of Correlations:Conformal Algebra and Multipoint Correlation Functions in 2D Statistical Models (Vl Dotsenko & V Fateev)On the Identification of Finite Operator Algebras in Two-dimensional Conformally Invariant Field Theories (P Christe & R Flume)Finite Size Scaling:Conformal Invariance, the Central Charge and Universal Finite Size Amplitudes at Criticality (H Blöte et al.)Universal Term in the Free Energy at a Critical Point and the Conformal Anomaly (I Affleck)Exact Surface and Wedge Exponents for Polymers in Two Dimensions (B Duplantier & H Saleur)Modular Invariance:Modular Invariant Partition Functions in Two Dimensions (A Cappelli et al.)Modular Invariant Partition Functions for Parafermionic Field Theories (D Gepner & Z Qiu)Discrete Symmetries of Conformal Theories (J-B Zuber)Connections With Integrable Systems:Exact Exponents for Infinitely many New Multicritical Points (D Huse)Automorphic Properties of Local Height Probabilities for Integrable Solid-on-solid Models (E Date et al.)Models with c = 1:Correlation Functions on the Critical Lines of the Baxter and Ashkin-Teller Models (L Kadanoff & A Brown)Supersymmetric Critical Phenomena and the Two Dimensional Gaussian Model (D Friedan & S Shenker)Curiosities at c=1 (P Ginsparg)Coulomb Gas Picture:Lattice Derivation of Modular Invariant Partition Functions on the Torus (V Pasquier)Vicinity of the Critical Point:Integrals of Motion in Scaling 3-state Potts Model Field Theory (A Zamolodchikov)Correlation Functions and Higher Topology:The Conformal Field Theory of Orbifolds (L Dixon et al.)Conformal and Current Algebras on a General Riemann Surface (T Eguchi & H Ooguri)and other papers Readership: Theoretical physicists in particle and statistical physics and mathematicians.

## Geometry and Analysis on Finite- and Infinite-dimensional Lie Groups

Publisher : Unknown

Release Date : 2002

Category : Finite groups

Total pages :357

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