Morita equivalence and continuous-trace C*-algebras / Iain Raeburn, Dana P. Williams.

Format:

Book

Author/Creator:

Raeburn, Iain, 1949- author.

Williams, Dana P., 1952- author.

Series:

Mathematical surveys and monographs ; no. 60.

Mathematical surveys and monographs, 0076-5376 ; volume 60

Language:

English

Subjects (All):

C*-algebras.

Physical Description:

1 online resource (345 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [1998]

Language Note:

English

Summary:

A modern treatment of this complex mathematical topic for students beginning research in operator algebras as well as mathematical physicists. Topics include the algebra of compact operators, sheaves, cohomology, the Brauer group and group actions, and the imprimivity theorem. The authors assume a knowledge of C*-algebras, the Gelfand-Naimark Theorem, continuous functional calculus, positivity, and the GNS- construction. Annotation copyrighted by Book News, Inc., Portland, OR

Contents:

""Contents""; ""Introduction""; ""1 The Algebra of Compact Operators""; ""2 Hilbert C*-Modules""; ""2.1 Hilbert Modules""; ""2.2 Bounded Maps on Hilbert Modules""; ""2.3 Multiplier Algebras""; ""2.4 Induced Representations""; ""3 Morita Equivalence""; ""3.1 Imprimitivity Bimodules""; ""3.2 Morita Equivalence""; ""3.3 The Rieffel Correspondence""; ""3.4 The External Tensor Product""; ""4 Sheaves, Cohomology, and Bundles""; ""4.1 Sheaf Cohomology""; ""4.2 Fibre Bundles""; ""4.3 The Dixmier-Douady Classification of Locally Trivial Bundles""; ""5 Continuous-Trace C*-Algebras""

""5.1 C*-Algebras with Hausdorff Spectrum""""5.2 Continuous-Trace C*-Algebras""; ""5.3 The Dixmier-Douady Classification of Continuous-Trace C*-Algebras""; ""5.4 Automorphisms of Continuous-Trace C*-Algebras""; ""5.5 Classification up to Stable Isomorphism""; ""6 Applications""; ""6.1 The Brauer Group""; ""6.2 Pull-back C*-Algebras""; ""6.3 Induced C*-Algebras""; ""7 Epilogue: The Brauer Group and Group Actions""; ""7.1 Dynamical Systems and Crossed Products""; ""7.2 The Equivariant Brauer Group""; ""7.3 The Brauer Group of a Point""; ""7.4 Group Cohomology and Moore Cohomology""

""7.5 The Brauer Group for Trivial Actions""""7.6 The Brauer Group for Free and Proper Actions""; ""7.7 The Structure of the Brauer Group""; ""A: The Spectrum""; ""A.1 States and Representations""; ""A.2 The Spectrum of a C*-Algebra""; ""A.3 The Dauns-Hofmann Theorem""; ""A.4 The State Space of a C*-Algebra""; ""B: Tensor Products of C*-Algebras""; ""B.1 The Spatial Tensor Product""; ""B.2 Fundamental Examples""; ""B.3 Other C*-Norms""; ""B.4 C*-Algebras with Hausdorff Spectrum""; ""B.5 Tensor Products of General C*-Algebras""; ""C: The Imprimitivity Theorem""

""C.1 Haar Measure and Measures on Homogeneous Spaces""""C.2 Vector-Valued Integration on Groups""; ""C.3 The Group C*-Algebra""; ""C.4 The Imprimitivity Theorem""; ""C.5 Induced Representations of Groups""; ""C.6 The Stone-von Neumann Theorem""; ""D: Miscellany""; ""D.1 Direct Limits""; ""D.2 The Inductive Limit Topology""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""J""; ""K""; ""L""; ""M""; ""N""; ""O""; ""P""; ""Q""; ""R""; ""S""; ""T""; ""U""; ""V""; ""W""; ""Bibliography""

Notes:

Description based upon print version of record.

Includes bibliographical references (pages 317-327) and index.

Description based on print version record.

ISBN:

1-4704-1287-X