A comparison type property for Cartan subalgebras

Abstract: Regularity properties of C*-algebras are vital for classification theory. In the C*-setting, finite nuclear dimension, tensorial absorption of the Jiang--Su algebra and strict comparison set the stage for Elliott's classification programme; these properties are known to be tightly related, as the (to a large extent confirmed) Toms--Winter conjecture predicts. On the dynamical side, analogues of these have been introduced for group actions, and it is not yet quite clear how these relate to the regularity properties of the crossed product. In this talk, we introduce a comparison type property in the context of Cartan subalgebras and study its relations to regularity properties of the ambient C*-algebra, and of the underlying dynamics, when the inclusion arises from a topological dynamical system. This talk is based on joint work (in progress) with Wilhelm Winter.

functional analysisoperator algebras

Audience: advanced learners

Functional analysis and operator algebras in Athens

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