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Structure Of The Standard Modules For The Affine Lie Algebra A1 1
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Book Synopsis Structure of the Standard Modules for the Affine Lie Algebra $A^{(1)}_1$ by : James Lepowsky
Download or read book Structure of the Standard Modules for the Affine Lie Algebra $A^{(1)}_1$ written by James Lepowsky and published by American Mathematical Soc.. This book was released on 1985 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: The affine Kac-Moody algebra $A_1 DEGREES{(1)}$ has served as a source of ideas in the representation theory of infinite-dimensional affine Lie algebras. This book develops the calculus of vertex operators to solve the problem of constructing all the standard $A_1 DEGREES{(1)}$-modules in the homogeneou
Book Synopsis Structures of the Level One Standard Modules for the Affine Lie Algebras $B_l^{(1)}$, $F_4^{(1)}$, and $G_2^{(1)}$ by : Marly Mandia
Download or read book Structures of the Level One Standard Modules for the Affine Lie Algebras $B_l^{(1)}$, $F_4^{(1)}$, and $G_2^{(1)}$ written by Marly Mandia and published by American Mathematical Soc.. This book was released on 1987 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lie Algebras and Related Topics by : Daniel J. Britten
Download or read book Lie Algebras and Related Topics written by Daniel J. Britten and published by American Mathematical Soc.. This book was released on 1986 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the Proceedings of the 1984 Canadian Mathematical Society's Summer Seminar, this book focuses on some advances in the theory of semisimple Lie algebras and some direct outgrowths of that theory. The following papers are of particular interest: an important survey article by R. Block and R. Wilson on restricted simple Lie algebras, a survey of universal enveloping algebras of semisimple Lie algebras by W. Borho, a course on Kac-Moody Lie algebras by I. G. Macdonald with an extensive bibliography of this field by Georgia Benkart, and a course on formal groups by M. Hazewinkel. Because of the expository surveys and courses, the book will be especially useful to graduate students in Lie theory, as well as to researchers in the field.
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 224 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.
Book Synopsis Lie Algebras and Related Topics by : Georgia Benkart
Download or read book Lie Algebras and Related Topics written by Georgia Benkart and published by American Mathematical Soc.. This book was released on 1990 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses the problem of determining the finite-dimensional simple Lie algebras over an algebraically closed field of characteristic $p>7$. This book includes topics such as Lie algebras of prime characteristic, algebraic groups, combinatorics and representation theory, and Kac-Moody and Virasoro algebras.
Book Synopsis Vertex Operators in Mathematics and Physics by : J. Lepowsky
Download or read book Vertex Operators in Mathematics and Physics written by J. Lepowsky and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: James Lepowsky t The search for symmetry in nature has for a long time provided representation theory with perhaps its chief motivation. According to the standard approach of Lie theory, one looks for infinitesimal symmetry -- Lie algebras of operators or concrete realizations of abstract Lie algebras. A central theme in this volume is the construction of affine Lie algebras using formal differential operators called vertex operators, which originally appeared in the dual-string theory. Since the precise description of vertex operators, in both mathematical and physical settings, requires a fair amount of notation, we do not attempt it in this introduction. Instead we refer the reader to the papers of Mandelstam, Goddard-Olive, Lepowsky-Wilson and Frenkel-Lepowsky-Meurman. We have tried to maintain consistency of terminology and to some extent notation in the articles herein. To help the reader we shall review some of the terminology. We also thought it might be useful to supplement an earlier fairly detailed exposition of ours [37] with a brief historical account of vertex operators in mathematics and their connection with affine algebras. Since we were involved in the development of the subject, the reader should be advised that what follows reflects our own understanding. For another view, see [29].1 t Partially supported by the National Science Foundation through the Mathematical Sciences Research Institute and NSF Grant MCS 83-01664. 1 We would like to thank Igor Frenkel for his valuable comments on the first draft of this introduction.
Book Synopsis Lie Algebras of Finite and Affine Type by : Roger William Carter
Download or read book Lie Algebras of Finite and Affine Type written by Roger William Carter and published by Cambridge University Press. This book was released on 2005-10-27 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough but relaxed mathematical treatment of Lie algebras.
Book Synopsis Lie Algebras, Vertex Operator Algebras and Their Applications by : Yi-Zhi Huang
Download or read book Lie Algebras, Vertex Operator Algebras and Their Applications written by Yi-Zhi Huang and published by American Mathematical Soc.. This book was released on 2007 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this book are based on talks given at the international conference 'Lie algebras, vertex operator algebras and their applications'. The focus of the papers is mainly on Lie algebras, quantum groups, vertex operator algebras and their applications to number theory, combinatorics and conformal field theory.
Book Synopsis Annihilating Fields of Standard Modules of $\mathfrak {sl}(2, \mathbb {C})^\sim $ and Combinatorial Identities by : Arne Meurman
Download or read book Annihilating Fields of Standard Modules of $\mathfrak {sl}(2, \mathbb {C})^\sim $ and Combinatorial Identities written by Arne Meurman and published by American Mathematical Soc.. This book was released on 1999 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the authors show that a set of local admissible fields generates a vertex algebra. For an affine Lie algebra $\tilde{\frak g}$, they construct the corresponding level $k$ vertex operator algebra and show that level $k$ highest weight $\tilde{\frak g}$-modules are modules for this vertex operator algebra. They determine the set of annihilating fields of level $k$ standard modules and study the corresponding loop $\tilde{\frak g}$-module--the set of relations that defines standard modules. In the case when $\tilde{\frak g}$ is of type $A{(1)} 1$, they construct bases of standard modules parameterized by colored partitions, and as a consequence, obtain a series of Rogers-Ramanujan type combinatorial identities.
Book Synopsis Integrable Systems in Quantum Field Theory and Statistical Mechanics by : M. Jimbo
Download or read book Integrable Systems in Quantum Field Theory and Statistical Mechanics written by M. Jimbo and published by Elsevier. This book was released on 2014-05-19 with total page 695 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrable Sys Quantum Field Theory
Download or read book Glasnik Matematički written by and published by . This book was released on 1998 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lie Algebras and Related Topics by : D. Winter
Download or read book Lie Algebras and Related Topics written by D. Winter and published by Springer. This book was released on 2006-11-14 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Recent Progress In Statistical Mechanics And Quantum Field Theory by : H Saleur
Download or read book Recent Progress In Statistical Mechanics And Quantum Field Theory written by H Saleur and published by World Scientific. This book was released on 1995-08-31 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: The following topics were covered: the study of renormalization group flows between field theories using the methods of quantum integrability, S-matrix theory and the thermodynamic Bethe Ansatz; impurity problems approached both from the point of view of conformal field theory and quantum integrability. This includes the Kondo effect and quantum wires; solvable models with 1/r² interactions (Haldane-Shastri models). Yangian symmetries in 1/r² models and in conformal field theories; correlation functions in integrable 1+1 field theories; integrability in three dimensions; conformal invariance and the quantum hall effect; supersymmetry in statistical mechanics; and relations to two-dimensional Yang-Mills and QCD.
Book Synopsis Topological and Geometrical Methods in Field Theory by : Jarmo Hietarinta
Download or read book Topological and Geometrical Methods in Field Theory written by Jarmo Hietarinta and published by . This book was released on 1986 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Yang-baxter Equations In Paris - Proceedings Of The Conference by : Jean-marie Maillard
Download or read book Yang-baxter Equations In Paris - Proceedings Of The Conference written by Jean-marie Maillard and published by World Scientific. This book was released on 1993-10-04 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :University of Minnesota. Institute for Mathematics and Its Applications Publisher :American Mathematical Soc. ISBN 13 :0821850962 Total Pages :378 pages Book Rating :4.8/5 (218 download)
Book Synopsis Singularities by : University of Minnesota. Institute for Mathematics and Its Applications
Download or read book Singularities written by University of Minnesota. Institute for Mathematics and Its Applications and published by American Mathematical Soc.. This book was released on 1989 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers the proceedings of the Institute for Mathematics and its Applications Participating Institutions Conference on Singularities, held at the University of Iowa in July 1986. Suitable for researchers in various aspects of singularity theory, this work provides an overview of the state of singularity theory and details work in several subareas.
Book Synopsis Introduction to Lie Algebras by : K. Erdmann
Download or read book Introduction to Lie Algebras written by K. Erdmann and published by Springer Science & Business Media. This book was released on 2006-09-28 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie groups and Lie algebras have become essential to many parts of mathematics and theoretical physics, with Lie algebras a central object of interest in their own right. This book provides an elementary introduction to Lie algebras based on a lecture course given to fourth-year undergraduates. The only prerequisite is some linear algebra and an appendix summarizes the main facts that are needed. The treatment is kept as simple as possible with no attempt at full generality. Numerous worked examples and exercises are provided to test understanding, along with more demanding problems, several of which have solutions. Introduction to Lie Algebras covers the core material required for almost all other work in Lie theory and provides a self-study guide suitable for undergraduate students in their final year and graduate students and researchers in mathematics and theoretical physics.
