A Universal Coefficient Theorem for Actions of Finite Groups on $\rm{C}^∗$-Algebras
Vol. 33 (2026), No. 1, Page 21-47.
Meyer, R.; Nadareishvili, G.
A Universal Coefficient Theorem for Actions of Finite Groups on $\rm{C}^∗$-Algebras
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]
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 $\rm{I}$ $\rm{C}^∗$-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.
Keywords: $\rm{C}^∗$-algebra classification, Universal Coefficient Theorem, Kirchberg algebra, bootstrap class, equivariant K-theory, triangulated categories, relative homological algebra.
Mathematics Subject Classification (2020): Primary 19K35; secondary 14L35.
Received: 2024-06-19
