Infinite Dimensional Lie Groups In Geometry And Representation Theory

Infinite Dimensional Lie Groups In Geometry And Representation Theory
Author :
Publisher : World Scientific
Total Pages : 174
Release :
ISBN-10 : 9789814488143
ISBN-13 : 9814488143
Rating : 4/5 (43 Downloads)

Synopsis Infinite Dimensional Lie Groups In Geometry And Representation Theory by : Augustin Banyaga

This book constitutes the proceedings of the 2000 Howard conference on “Infinite Dimensional Lie Groups in Geometry and Representation Theory”. It presents some important recent developments in this area. It opens with a topological characterization of regular groups, treats among other topics the integrability problem of various infinite dimensional Lie algebras, presents substantial contributions to important subjects in modern geometry, and concludes with interesting applications to representation theory. The book should be a new source of inspiration for advanced graduate students and established researchers in the field of geometry and its applications to mathematical physics.

Infinite Dimensional Groups with Applications

Infinite Dimensional Groups with Applications
Author :
Publisher : Springer Science & Business Media
Total Pages : 406
Release :
ISBN-10 : 0387962166
ISBN-13 : 9780387962160
Rating : 4/5 (66 Downloads)

Synopsis Infinite Dimensional Groups with Applications by : Victor Kac

This volume records most of the talks given at the Conference on Infinite-dimensional Groups held at the Mathematical Sciences Research Institute at Berkeley, California, May 10-May 15, 1984, as a part of the special program on Kac-Moody Lie algebras. The purpose of the conference was to review recent developments of the theory of infinite-dimensional groups and its applications. The present collection concentrates on three very active, interrelated directions of the field: general Kac-Moody groups, gauge groups (especially loop groups) and diffeomorphism groups. I would like to express my thanks to the MSRI for sponsoring the meeting, to Ms. Faye Yeager for excellent typing, to the authors for their manuscripts, and to Springer-Verlag for publishing this volume. V. Kac INFINITE DIMENSIONAL GROUPS WITH APPLICATIONS CONTENTS The Lie Group Structure of M. Adams. T. Ratiu 1 Diffeomorphism Groups and & R. Schmid Invertible Fourier Integral Operators with Applications On Landau-Lifshitz Equation and E. Date 71 Infinite Dimensional Groups Flat Manifolds and Infinite D. S. Freed 83 Dimensional Kahler Geometry Positive-Energy Representations R. Goodman 125 of the Group of Diffeomorphisms of the Circle Instantons and Harmonic Maps M. A. Guest 137 A Coxeter Group Approach to Z. Haddad 157 Schubert Varieties Constructing Groups Associated to V. G. Kac 167 Infinite-Dimensional Lie Algebras I. Kaplansky 217 Harish-Chandra Modules Over the Virasoro Algebra & L. J. Santharoubane 233 Rational Homotopy Theory of Flag S.

Lie Theory

Lie Theory
Author :
Publisher : Springer Science & Business Media
Total Pages : 341
Release :
ISBN-10 : 9780817681920
ISBN-13 : 0817681922
Rating : 4/5 (20 Downloads)

Synopsis Lie Theory by : Jean-Philippe Anker

* First of three independent, self-contained volumes under the general title, "Lie Theory," featuring original results and survey work from renowned mathematicians. * Contains J. C. Jantzen's "Nilpotent Orbits in Representation Theory," and K.-H. Neeb's "Infinite Dimensional Groups and their Representations." * Comprehensive treatments of the relevant geometry of orbits in Lie algebras, or their duals, and the correspondence to representations. * Should benefit graduate students and researchers in mathematics and mathematical physics.

Introduction to Finite and Infinite Dimensional Lie (Super)algebras

Introduction to Finite and Infinite Dimensional Lie (Super)algebras
Author :
Publisher : Academic Press
Total Pages : 514
Release :
ISBN-10 : 9780128046838
ISBN-13 : 012804683X
Rating : 4/5 (38 Downloads)

Synopsis Introduction to Finite and Infinite Dimensional Lie (Super)algebras by : Neelacanta Sthanumoorthy

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

The Geometry of Infinite-Dimensional Groups

The Geometry of Infinite-Dimensional Groups
Author :
Publisher : Springer Science & Business Media
Total Pages : 304
Release :
ISBN-10 : 9783540772637
ISBN-13 : 3540772634
Rating : 4/5 (37 Downloads)

Synopsis The Geometry of Infinite-Dimensional Groups by : Boris Khesin

This monograph gives an overview of various classes of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrable systems, gauge theory, and complex geometry. The text includes many exercises and open questions.

Infinite-Dimensional Lie Groups

Infinite-Dimensional Lie Groups
Author :
Publisher : American Mathematical Soc.
Total Pages : 434
Release :
ISBN-10 : 9781470426354
ISBN-13 : 1470426358
Rating : 4/5 (54 Downloads)

Synopsis Infinite-Dimensional Lie Groups by : Hideki Omori

This book develops, from the viewpoint of abstract group theory, a general theory of infinite-dimensional Lie groups involving the implicit function theorem and the Frobenius theorem. Omori treats as infinite-dimensional Lie groups all the real, primitive, infinite transformation groups studied by E. Cartan. The book discusses several noncommutative algebras such as Weyl algebras and algebras of quantum groups and their automorphism groups. The notion of a noncommutative manifold is described, and the deformation quantization of certain algebras is discussed from the viewpoint of Lie algebras. This edition is a revised version of the book of the same title published in Japanese in 1979.

Representation Theory of Lie Groups

Representation Theory of Lie Groups
Author :
Publisher : Cambridge University Press
Total Pages : 349
Release :
ISBN-10 : 9780521226363
ISBN-13 : 0521226368
Rating : 4/5 (63 Downloads)

Synopsis Representation Theory of Lie Groups by : M. F. Atiyah

In 1977 a symposium was held in Oxford to introduce Lie groups and their representations to non-specialists.

Introduction to Lie Algebras and Representation Theory

Introduction to Lie Algebras and Representation Theory
Author :
Publisher : Springer Science & Business Media
Total Pages : 189
Release :
ISBN-10 : 9781461263982
ISBN-13 : 1461263980
Rating : 4/5 (82 Downloads)

Synopsis Introduction to Lie Algebras and Representation Theory by : J.E. Humphreys

This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms, euclidean spaces, and tensor products of vector spaces) is presupposed, as well as some acquaintance with the methods of abstract algebra. The first four chapters might well be read by a bright undergraduate; however, the remaining three chapters are admittedly a little more demanding. Besides being useful in many parts of mathematics and physics, the theory of semisimple Lie algebras is inherently attractive, combining as it does a certain amount of depth and a satisfying degree of completeness in its basic results. Since Jacobson's book appeared a decade ago, improvements have been made even in the classical parts of the theory. I have tried to incor porate some of them here and to provide easier access to the subject for non-specialists. For the specialist, the following features should be noted: (I) The Jordan-Chevalley decomposition of linear transformations is emphasized, with "toral" subalgebras replacing the more traditional Cartan subalgebras in the semisimple case. (2) The conjugacy theorem for Cartan subalgebras is proved (following D. J. Winter and G. D. Mostow) by elementary Lie algebra methods, avoiding the use of algebraic geometry.

Infinite Dimensional Lie Algebras

Infinite Dimensional Lie Algebras
Author :
Publisher : Springer Science & Business Media
Total Pages : 267
Release :
ISBN-10 : 9781475713824
ISBN-13 : 1475713827
Rating : 4/5 (24 Downloads)

Synopsis Infinite Dimensional Lie Algebras by : Victor G. Kac

An Introduction to Lie Groups and Lie Algebras

An Introduction to Lie Groups and Lie Algebras
Author :
Publisher : Cambridge University Press
Total Pages : 237
Release :
ISBN-10 : 9780521889698
ISBN-13 : 0521889693
Rating : 4/5 (98 Downloads)

Synopsis An Introduction to Lie Groups and Lie Algebras by : Alexander A. Kirillov

This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.