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Central sequence C*-algebras and tensorial absorption of the Jiang–Su algebra

2014
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Journal für die Reine und Angewandte Mathematik
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We study properties of the central sequence algebra A ω ∩ A of a C *algebra A, and we present an alternative approach to a recent result of Matui and Sato. They prove that every unital separable simple nuclear C * -algebra, whose trace simplex is finite dimensional, tensorially absorbs the Jiang-Su algebra if and only if it has the strict comparison property. We extend their result to the case where the extreme boundary of the trace simplex is closed and of finite topological dimension. We are

doi:10.1515/crelle-2012-0118
fatcat:ess5jjt4znecfbdixgtjnpxc3y