Reduced twisted crossed products over C*-simple groups

Rasmus Sylvester Bryder; Matthew Kennedy

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arXiv · 1602.01533

Reduced twisted crossed products over C*-simple groups

Rasmus Sylvester Bryder·Matthew Kennedy

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Abstract

We consider reduced crossed products of twisted C*-dynamical systems over C*-simple groups. We prove there is a bijective correspondence between maximal ideals of the reduced crossed product and maximal invariant ideals of the underlying C*-algebra, and a bijective correspondence between tracial states on the reduced crossed product and invariant tracial states on the underlying C*-algebra. In particular, the reduced crossed product is simple if and only if the underlying C*-algebra has no proper non-trivial invariant ideals, and the reduced crossed product has a unique tracial state if and only if the underlying C*-algebra has a unique invariant tracial state. We also show that the reduced crossed product satisfies an averaging property analogous to Powers' averaging property.

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Rasmus Sylvester Bryder, Matthew Kennedy. 2016-02-04. Reduced twisted crossed products over C*-simple groups. https://arxiv.org/abs/1602.01533

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