Current Algebras on Riemann Surfaces : New Results and Applications / Oleg K. Sheinman.

Format:

Book

Author/Creator:

Sheinman, Oleg K., author.

Series:

De Gruyter Expositions in Mathematics

De Gruyter Expositions in Mathematics ; 58

Language:

English

Subjects (All):

Lie algebras.

Riemann surfaces.

Physical Description:

1 online resource (164 p.)

Edition:

1st ed.

Place of Publication:

Berlin ; Boston : De Gruyter, [2012]

Language Note:

English

Summary:

This monograph is an introduction into a new and fast developing field on the crossroads of infinite-dimensional Lie algebra theory and contemporary mathematical physics. It contains a self-consistent presentation of the theory of Krichever-Novikov algebras, Lax operator algebras, their interaction, representation theory, relations to moduli spaces of Riemann surfaces and holomorphic vector bundles on them, to Lax integrable systems, and conformal field theory. For beginners, the book provides a short way to join in the investigations in these fields. For experts, it sums up the recent advances in the theory of almost graded infinite-dimensional Lie algebras and their applications. The book may serve as a base for semester lecture courses on finite-dimensional integrable systems, conformal field theory, almost graded Lie algebras. Majority of results are presented for the first time in the form of monograph.

Contents:

Front matter

Preface

Contents

Chapter 1. Krichever-Novikov algebras: basic definitions and structure theory

Chapter 2. Fermion representations and Sugawara construction

Chapter 3. Projective flat connections on the moduli space of punctured Riemann surfaces and the Knizhnik-Zamolodchikov equation

Chapter 4. Lax operator algebras

Chapter 5. Lax equations with a spectral parameter on Riemann surfaces, and their hierarchies

Chapter 6. Lax integrable systems and conformal field theory

Bibliography

Notation

Index

Notes:

Description based upon print version of record.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9781283856690

1283856697

9783110264524

3110264528

OCLC:

819508472