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Functoriality of Rieffel's Generalised Fixed-Point Algebras for Proper Actions

Authors
  • Huef, Astrid an
  • Raeburn, Iain
  • Williams, Dana
Type
Preprint
Publication Date
Sep 15, 2009
Submission Date
Sep 15, 2009
Source
arXiv
License
Yellow
External links

Abstract

We consider two categories of C*-algebras; in the first, the isomorphisms are ordinary isomorphisms, and in the second, the isomorphisms are Morita equivalences. We show how these two categories, and categories of dynamical systems based on them, crop up in a variety of C*-algebraic contexts. We show that Rieffel's construction of a fixed-point algebra for a proper action can be made into functors defined on these categories, and that his Morita equivalence then gives a natural isomorphism between these functors and crossed-product functors. These results have interesting applications to non-abelian duality for crossed products.

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