A categorical approach to imprimitivity theorems for C*-dynamical systems
著者
書誌事項
A categorical approach to imprimitivity theorems for C*-dynamical systems
（Memoirs of the American Mathematical Society, no. 850）
American Mathematical Society, c2006
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注記
Includes bibliographical references (p. 167-169)
"Volume 180, number 850 (fourth of 5 numbers)"
内容説明・目次
内容説明
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.
目次
Introduction Right-Hilbert bimodules The categories The functors The natural equivalences Applications Appendix A. Crossed products by actions and coactions Appendix B. The imprimitivity theorems of Green and Mansfield Appendix C. function spaces Appendix. Bibliography.
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