Lie Groups and Lie Algebras I Foundations of Lie Theory. Lie Transformation Groups

Abstract

The first in a series of volumes devoted to the theory of Lie groups and Lie algebras, covering research results of the last few decades. The first part of the book deals with the foundations of the theory, based on the classical global approach of Chevalley, followed by an exposition of the alternative approach via the universal algebra and the Campbell-Hausdorff formula. The second, more advanced part treats Lie transformation groups covering such topics as the properties of orbits and stabilizers, homogeneous fibre bundles, Frobenius duality, groups of automorphisms of geometric structures, Lie algebras of vector fields and the existence of slices. The book contains numerous examples and describes connections to topology, differential geometry, analysis and applications, and thus is of great interest to graduate students and researchers in mathematics and theoretical physics.