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تسجيل مستخدم جديدRokhlin dimension: absorption of model actions
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تأليف
Gabor Szabo
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In this paper, we establish a connection between Rokhlin dimension and the absorption of certain model actions on strongly self-absorbing C*-algebras. Namely, as to be made precise in the paper, let $G$ be a well-behaved locally compact group. If $mathcal D$ is a strongly self-absorbing C*-algebra, and $alpha: Gcurvearrowright A$ is an action on a separable, $mathcal D$-absorbing C*-algebra that has finite Rokhlin dimension with commuting towers, then $alpha$ tensorially absorbs every semi-strongly self-absorbing $G$-actions on $mathcal D$. This contains several existing results of similar nature as special cases. We will in fact prove a more general version of this theorem, which is intended for use in subsequent work. We will then discuss some non-trivial applications. Most notably it is shown that for any $kgeq 1$ and on any strongly self-absorbing Kirchberg algebra, there exists a unique $mathbb R^k$-action having finite Rokhlin dimension with commuting towers up to (very strong) cocycle conjugacy.
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