Description
Book SynopsisA treatise on Lie groups in which a modern point of view was adopted systematically, namely, that a continuous group can be regarded as a global object. This book incorporates a broad range of topics, such as the covering spaces of topological spaces, analytic manifolds, and integration of complete systems of differential equations on a manifold.
Trade Review"Chevalley's most important contribution to mathematics is certainly his work on group theory ... [Theory of Lie Groups] was the first systematic exposition of the foundations of Lie group theory consistently adopting the global viewpoint, based on the notion of analytic manifold. This book remained the basic reference on Lie groups for at least two decades."--Bulletin of the American Mathematical Society
Table of ContentsINTRODUCTION vii I. THE CLASSICAL LINEAR GROUPS 1 II. TOPOLOGICAL GROUPS 25 III. MANIFOLDS 68 IV. ANALYTIC GROUPS. LIE GROUPS 99 V. THE DIFFERENTIAL CALCULUS 0F CARTAN 139 VI. COMPACT LIE GROUPS AND THEIR REPRESENTATIONS 171 INDEX 215
