Overview

The book by Gorbatsevich, Onishchik and Vinberg is the firstin a series of volumes devoted to the theory of Lie groupsand Lie algebras.The first part of the book deals with the foundations of thetheory based on the classical global approach of Chevalleyfollowed by an exposition of the alternative approach viathe universal algebra and the Campbell-Hausdorff formula. Italso contains a survey of certain generalizations of Liegroups.The second more advanced part treats the topic of Lietransformation groups covering e.g. properties of orbits andstabilizers, homogeneous fibre bundles, Frobenius duality,groups ofautomorphisms of geometric structures, Liealgebras of vector fields and theexistence of slices. Thework of the last decades including the most recentresearch results is covered.The book contains numerous examples and describesconnections with topology, differential geometry, analysisand applications. It will be of great interest to graduatestudents and researchers in mathematics and theoreticalphysics.

Full Product Details

Author:   V.V. Gorbatsevich ,  A.L. Onishchik ,  T. Kozlowski ,  A.L. Onishchik
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   1993 ed.
Volume:   20
Dimensions:   Width: 15.50cm , Height: 1.80cm , Length: 23.50cm
Weight:   0.547kg
ISBN:  

9783540186977

ISBN 10:   3540186972
Pages:   238
Publication Date:   15 April 1993
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

I.Foundations of Lie Theory.- 1. Basic Notions.- 2. The Relation Between Lie Groups and Lie Algebras.- 3. The Universal Enveloping Algebra.- 4. Generalizations of Lie Groups.- II. Lie Transformation Groups.- 1. Lie Group Actions on Manifolds.- 2. Transitive Actions.- 3. Actions of Compact Lie Groups.- 4. Homogeneous Spaces of Nilpotent and Solvable Groups.- 5. Compact Homogeneous Spaces.- 6. Actions of Lie Groups on Low-dimensional Manifolds.

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