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Download A Categorical Approach to Imprimitivity Theorems for $c^*$-dynamical Systems (Memoirs of the American Mathematical Society) epub

by S. Kaliszewski John Quigg and Iain Raeburn Siegfried Echterhoff




Imprimitivity theorems provide a fundamental tool for studying the representation theory and structure of crossed-product $C^*$-algebras. In this work, we show that the Imprimitivity Theorem for induced algebras, Green's Imprimitivity Theorem for actions of groups, and Mansfield's Imprimitivity Theorem for coactions of groups can all be viewed as natural equivalences between various crossed-product functors among certain equivariant categories. The categories involved have $C^*$-algebras with actions or coactions (or both) of a fixed locally compact group $G$ as their objects, and equivariant equivalence classes of right-Hilbert bimodules as their morphisms. Composition is given by the balanced tensor product of bimodules. The functors involved arise from taking crossed products; restricting, inflating, and decomposing actions and coactions; inducing actions; and various combinations of these. Several applications of this categorical approach are also presented, including some intriguing relationships between the Green and Mansfield bimodules, and between restriction and induction of representations.
Download A Categorical Approach to Imprimitivity Theorems for $c^*$-dynamical Systems (Memoirs of the American Mathematical Society) epub
ISBN: 0821838571
ISBN13: 978-0821838570
Category: Science
Subcategory: Mathematics
Author: S. Kaliszewski John Quigg and Iain Raeburn Siegfried Echterhoff
Language: English
Publisher: American Mathematical Society (January 31, 2006)
Pages: 169 pages
ePUB size: 1709 kb
FB2 size: 1506 kb
Rating: 4.7
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