Lie Algebraic Methods in Integrable Systems

Amit K. Roy-Chowdhury

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English

Chapman & Hall/CRC
28 September 1999

Algebra; Non-linear science

Series: Chapman & Hall/CRC Research Notes in Mathematics Series

Over the last thirty years, the subject of nonlinear integrable systems has grown into a full-fledged research topic. In the last decade, Lie algebraic methods have grown in importance to various fields of theoretical research and worked to establish close relations between apparently unrelated systems.

The various ideas associated with Lie algebra and Lie groups can be used to form a particularly elegant approach to the properties of nonlinear systems. In this volume, the author exposes the basic techniques of using Lie algebraic concepts to explore the domain of nonlinear integrable systems. His emphasis is not on developing a rigorous mathematical basis, but on using Lie algebraic methods as an effective tool.

The book begins by establishing a practical basis in Lie algebra, including discussions of structure Lie, loop, and Virasor groups, quantum tori and Kac-Moody algebras, and gradation. It then offers a detailed discussion of prolongation structure and its representation theory, the orbit approach-for both finite and infinite dimension Lie algebra. The author also presents the modern approach to symmetries of integrable systems, including important new ideas in symmetry analysis, such as gauge transformations, and the ""soldering"" approach. He then moves to Hamiltonian structure, where he presents the Drinfeld-Sokolov approach, the Lie algebraic approach, Kupershmidt's approach, Hamiltonian reductions and the Gelfand Dikii formula. He concludes his treatment of Lie algebraic methods with a discussion of the classical r-matrix, its use, and its relations to double Lie algebra and the KP equation.

By: Amit K. Roy-Chowdhury
Imprint: Chapman & Hall/CRC
Country of Publication: United States
Volume: 415
Dimensions: Height: 234mm, Width: 156mm, Spine: 19mm
Weight: 680g
ISBN: 9781584880370
ISBN 10: 1584880376
Series: Chapman & Hall/CRC Research Notes in Mathematics Series
Pages: 366
Publication Date: 28 September 1999
Audience: College/higher education , Professional and scholarly , Professional & Vocational , A / AS level , Further / Higher Education
Format: Paperback
Publisher's Status: Active

Amit K. Roy-Chowdhury (University of California, Riverside, USA) (Author)

Reviews for Lie Algebraic Methods in Integrable Systems

"""Lie theory and algebraic geometry have played a unifying role in integrable theory since its early rebirth some 30 years ago. They have transformed a mosaic of old examples, due to the masters like Hamilton, Jacobi and Kowalewski, and new examples into general methods and statements. The book under review addresses a number of these topics… contains a variety of interesting topics: some are expained in a user-friendly and elementary way, and others are taken directly from research papers."" -Pierre Van Moerbeke, in The London Mathematical Society"