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

Astrid an Huef; Iain Raeburn; Dana Williams

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arXiv · 0909.2860

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

Astrid an Huef·Iain Raeburn·Dana Williams

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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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Astrid an Huef, Iain Raeburn, Dana Williams. 2009-09-15. Functoriality of Rieffel's Generalised Fixed-Point Algebras for Proper Actions. https://arxiv.org/abs/0909.2860

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