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Group actions on C*-algebras and obstruction theory

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OAS - Operator algebras: subfactors and their applications

This talk gives an account of the roles in group actions on C*-algebras played by the classical obstruction theory for fiber bundles. More specifically, I discuss the following deciding problems:

(1) whether a given 2-cocycle action is equivalent to an ordinary action or not,
(2) whether a given 1-cocycle of an action is an (asymptotic) coboundary or not,
(3) whether two given actions are cocycle conjugate or not.

The idea works well for poly-Z groups on Kirchberg algebras.

This is joint work with Hiroki Matui.

This talk is part of the Isaac Newton Institute Seminar Series series.

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