Lie Groups and Lie Algebras I

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.