The Structure of compact groups : a primer for the student, a handbook for the expert

The Structure of compact groups : a primer for the student, a handbook for the expert / Karl H. Hofmann, Sidney A. Morris.

Dealing with subject matter of compact groups that is frequently cited in fields like algebra, topology, functional analysis, and theoretical physics, this book - now in its third revised and augmented edition - has been conceived with the dual purpose of providing a text book for upper level gradua...

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Bibliographic Details
Main Authors: Hofmann, Karl Heinrich (Author), Morris, Sidney A., 1947- (Author)
Format: eBook
Language:English
Published: Berlin : De Gruyter, 2013.
Edition:3rd edition, rev. and augmented.
Series:De Gruyter studies in mathematics ; 25.
Subjects:
Compact groups.
MATHEMATICS > Algebra > Intermediate.
Compact groups
Online Access:Click for online access
Table of Contents:
  • Chapter 1. Basic Topics and Examples; Definitions and Elementary Examples; Actions, Subgroups, Quotient Spaces; Products of Compact Groups; Applications to Abelian Groups; Projective Limits; Totally Disconnected Compact Groups; Some Duality Theory; Postscript; References for this Chapter-Additional Reading; Chapter 2. The Basic Representation Theory of Compact Groups; Some Basic Representation Theory for Compact Groups; The Haar Integral; Consequences of Haar Measure; The Main Theorem on Hilbert Modules for Compact Groups; Postscript; References for this Chapter-Additional Reading.
  • Chapter 3. The Ideas of Peter and WeylPart 1: The Classical Theorem of Peter and Weyl; An Excursion into Linear Algebra; The G-modules E'
  • "E, Hom(E, E) and Hom(E, E)'; The Fine Structure of R(G, K); Part 2: The General Theory of G-Modules; Vector Valued Integration; The First Application: The Averaging Operator; Compact Groups Acting on Convex Cones; More Module Actions, Convolutions; Complexification of Real Representations; Postscript; References for this Chapter-Additional Reading; Chapter 4. Characters; Part 1: Characters of Finite Dimensional Representations.
  • Part 2: The Structure Theorem of EfinCyclic Modules; Postscript; References for this Chapter-Additional Reading; Chapter 5. Linear Lie Groups; Preliminaries; The Exponential Function and the Logarithm; Differentiating the Exponential Function in a Banach Algebra; Local Groups for the Campbell-Hausdorff Multiplication; Subgroups of A-1 and Linear Lie Groups; Analytic Groups; The Intrinsic Exponential Function of a Linear Lie Group; The Adjoint Representation of a Linear Lie Group; Subalgebras, Ideals, Lie Subgroups, Normal Lie Subgroups; Normalizers, Centralizers, Centers.
  • The Commutator SubgroupForced Continuity of Morphisms between Lie Groups; Quotients of Linear Lie Groups; The Topological Splitting Theorem for Normal Vector Subgroups; Postscript; References for this Chapter-Additional Reading; Chapter 6. Compact Lie Groups; Compact Lie algebras; The Commutator Subgroup of a Compact Lie Group; The Structure Theorem for Compact Lie Groups; Maximal Tori; The Second Structure Theorem for Connected Compact Lie Groups; Compact Abelian Lie Groups and their Linear Actions; Action of a Maximal Torus on the Lie Algebra; The Weyl Group Revisited.
  • The Commutator Subgroup of Connected Compact Lie GroupsOn the Automorphism Group of a Compact Lie Group; Covering Groups of Disconnected Compact Lie Groups; Auerbach's Generation Theorem; The Topology of Connected Compact Lie Groups; Postscript; References for this Chapter-Additional Reading; Chapter 7. Duality of Abelian Topological Groups; The Compact Open Topology and Hom-Groups; Local Compactness and Duality of Abelian Topological Groups; Basic Functorial Aspects of Duality; The Annihilator Mechanism; Character Groups of Topological Vector Spaces; The Exponential Function.

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