The Structure of Compact Groups
From Book News, Inc. Following the first four chapters, which comprise the body of an introductory course on compact groups, the volume addresses the general theory of (linear) Lie groups; the structure of compact Lie groups; duality for abelian topological groups; compact abelian groups; the structure of compact groups and their actions; the structure of free compact groups; and cardinal invariants of compact groups. The initial chapters are for the beginning graduate student who has had basic analysis, algebra, elementary functional analysis up through the elements of Banach spaces and Banach algebras, and possesses a background in point set topology. Later chapters require more background knowledge, including some algebraic topology. The volume is useful for students and also for mathematicians in various specialties who want material on compact groups that is otherwise difficult to access. Book News, Inc.®, Portland, OR
Synopsis The theme of this work is the structure theory of compact groups. It presents an introduction to linear Lie groups and a substantial body of material on compact Lie groups. The authors' approach is distinctive in so far as they define a linear Lie group as a particular subgroup of the multiplicative group of a Banach algebra. Compact Lie groups are recognized at an early stage as being linear Lie groups. This approach avoids the use of machinery on manifolds. The text is intended to be...