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arXiv · 2406.11787

A universal coefficient theorem for actions of finite groups on C*-algebras

Ralf Meyer·George Nadareishvili
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Abstract

The equivariant bootstrap class in the Kasparov category of actions of a finite group G consists of those actions that are equivalent to one on a Type I C*-algebra. Using a result by Arano and Kubota, we show that this bootstrap class is already generated by the continuous functions on G/H for all cyclic subgroups H of G. Then we prove a Universal Coefficient Theorem for the localisation of this bootstrap class at the group order |G|. This allows us to classify certain G-actions on stable Kirchberg algebras up to cocycle conjugacy.

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Ralf Meyer, George Nadareishvili. 2024-06-17. A universal coefficient theorem for actions of finite groups on C*-algebras. https://arxiv.org/abs/2406.11787

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