**Author**: Edward Frenkel

**Publisher:** American Mathematical Soc.

**Format:** PDF, ePub, Mobi

**Category : **Mathematics

**Languages : **en

**Pages : **418

**View:** 2924

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*tag: Vertex Algebras And Algebraic Curves book download free, Vertex Algebras And Algebraic Curves book download in PDF, Vertex Algebras And Algebraic Curves epub books download free, book download online, Vertex Algebras And Algebraic Curves ebook download, download Vertex Algebras And Algebraic Curves ebook, Vertex Algebras And Algebraic Curves pdf download, Vertex Algebras And Algebraic Curves full book*
**Book Description:**
Vertex algebras are algebraic objects that encapsulate the concept of operator product expansion from two-dimensional conformal field theory. Vertex algebras are fast becoming ubiquitous in many areas of modern mathematics, with applications to representation theory, algebraic geometry, the theory of finite groups, modular functions, topology, integrable systems, and combinatorics. This book is an introduction to the theory of vertex algebras with a particular emphasis on the relationship with the geometry of algebraic curves. The notion of a vertex algebra is introduced in a coordinate-independent way, so that vertex operators become well defined on arbitrary smooth algebraic curves, possibly equipped with additional data, such as a vector bundle. Vertex algebras then appear as the algebraic objects encoding the geometric structure of various moduli spaces associated with algebraic curves. Therefore they may be used to give a geometric interpretation of various questions of representation theory. The book contains many original results, introduces important new concepts, and brings new insights into the theory of vertex algebras. The authors have made a great effort to make the book self-contained and accessible to readers of all backgrounds. Reviewers of the first edition anticipated that it would have a long-lasting influence on this exciting field of mathematics and would be very useful for graduate students and researchers interested in the subject. This second edition, substantially improved and expanded, includes several new topics, in particular an introduction to the Beilinson-Drinfeld theory of factorization algebras and the geometric Langlands correspondence.

**Author**: George Lusztig

**Publisher:** Springer Science & Business Media

**Format:** PDF, Mobi

**Category : **Mathematics

**Languages : **en

**Pages : **352

**View:** 2125

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*tag: Introduction To Quantum Groups book download free, Introduction To Quantum Groups book download in PDF, Introduction To Quantum Groups epub books download free, book download online, Introduction To Quantum Groups ebook download, download Introduction To Quantum Groups ebook, Introduction To Quantum Groups pdf download, Introduction To Quantum Groups full book*
**Book Description:**
The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical basis with rather remarkable properties. This book will be of interest to mathematicians working in the representation theory of Lie groups and Lie algebras, knot theorists and to theoretical physicists and graduate students. Since large parts of the book are independent of the theory of perverse sheaves, the book could also be used as a text book.

**Author**: Robert V. Moody

**Publisher:** Wiley-Interscience

**Format:** PDF

**Category : **Mathematics

**Languages : **en

**Pages : **760

**View:** 6367

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*tag: Lie Algebras With Triangular Decompositions book download free, Lie Algebras With Triangular Decompositions book download in PDF, Lie Algebras With Triangular Decompositions epub books download free, book download online, Lie Algebras With Triangular Decompositions ebook download, download Lie Algebras With Triangular Decompositions ebook, Lie Algebras With Triangular Decompositions pdf download, Lie Algebras With Triangular Decompositions full book*
**Book Description:**
Imparts a self-contained development of the algebraic theory of Kac-Moody algebras, their representations and close relatives--the Virasoro and Heisenberg algebras. Focuses on developing the theory of triangular decompositions and part of the Kac-Moody theory not specific to the affine case. Also covers lattices, and finite root systems, infinite-dimensional theory, Weyl groups and conjugacy theorems.

**Author**: John F. Cornwell

**Publisher:** Academic Press

**Format:** PDF, ePub, Docs

**Category : **Science

**Languages : **en

**Pages : **361

**View:** 638

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*tag: Group Theory In Physics book download free, Group Theory In Physics book download in PDF, Group Theory In Physics epub books download free, book download online, Group Theory In Physics ebook download, download Group Theory In Physics ebook, Group Theory In Physics pdf download, Group Theory In Physics full book*
**Book Description:**
This book, an abridgment of Volumes I and II of the highly respected Group Theory in Physics, presents a carefully constructed introduction to group theory and its applications in physics. The book provides anintroduction to and description of the most important basic ideas and the role that they play in physical problems. The clearly written text contains many pertinent examples that illustrate the topics, even for those with no background in group theory.This work presents important mathematical developments to theoretical physicists in a form that is easy to comprehend and appreciate. Finite groups, Lie groups, Lie algebras, semi-simple Lie algebras, crystallographic point groups and crystallographic space groups, electronic energy bands in solids, atomic physics, symmetry schemes for fundamental particles, and quantum mechanics are all covered in this compact new edition. Covers both group theory and the theory of Lie algebras Includes studies of solid state physics, atomic physics, and fundamental particle physics Contains a comprehensive index Provides extensive examples

**Author**: Vladislav Kharchenko

**Publisher:** Springer

**Format:** PDF, ePub, Mobi

**Category : **Mathematics

**Languages : **en

**Pages : **302

**View:** 1144

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*tag: Quantum Lie Theory book download free, Quantum Lie Theory book download in PDF, Quantum Lie Theory epub books download free, book download online, Quantum Lie Theory ebook download, download Quantum Lie Theory ebook, Quantum Lie Theory pdf download, Quantum Lie Theory full book*
**Book Description:**
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.