Cuntz-Krieger uniqueness theorem for crossed products by Hilbert bimodules

Abstract

It is shown that a C*-algebra generated by any faithful covariant representation of a Hilbert bimodule X is canonically isomorphic to the crossed product associated to X provided that Rieffel's induced representation functor X-ind is topologically free. It is discussed how this result could be applied to universal C*-algebras generated by relations with a circle gauge action. In particular, it leads to generalizations of isomorphism theorems for various crossed products, and is shown to be equivalent to Cuntz-Krieger uniqueness theorem for finite graph C*-algebras (on that occasion an intriguing realization of Cuntz-Krieger algebras as crossed products by Exel's interactions is discovered).

This paper has been withdrawn by the author. The results of the paper are presented in a more accurate and extended form in the following published papers: Topological freeness for Hilbert bimodules (arXiv:1212.0361), Crossed products for interactions and graph algebras (arXiv:1301.5125), Ideal structure of crossed products by endomorphisms via reversible extensions of C*-dynamical systems (arXiv:1404.4928)

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Cited by in corpus (5)

• Crossed products by endomorphisms and reduction of relations in relative Cuntz-Pimsner algebras
• Exel and Stacey crossed products, and Cuntz-Pimsner algebras
• Stacey crossed products associated to Exel systems
• The structure of crossed products by endomorphisms
• C*-dynamical systems associated to Graph C*-Algebras