Strongly self-absorbing C*-dynamical systems

TL;DR

This paper extends the concept of strongly self-absorbing C*-algebras to group actions, establishing an equivariant McDuff-type theorem that characterizes when a C*-dynamical system absorbs a strongly self-absorbing action.

Contribution

It introduces strongly self-absorbing actions of groups on C*-algebras and proves an equivariant absorption theorem generalizing existing non-equivariant results.

Findings

Established the notion of strongly self-absorbing actions.

Proved an equivariant McDuff-type absorption theorem.

Provided examples of strongly self-absorbing actions.

Abstract

We introduce and study strongly self-absorbing actions of locally compact groups on C*-algebras. This is an equivariant generalization of a strongly self-absorbing C*-algebra to the setting of C*-dynamical systems. The main result is the following equivariant McDuff-type absorption theorem: A cocycle action $(\alpha,u): G\curvearrowright A$ on a separable C*-algebra is cocycle conjugate to its tensorial stabilization with a strongly self-absorbing action $\gamma: G\curvearrowright\mathcal{D}$, if and only if there exists an equivariant and unital $*$-homomorphism from $\mathcal{D}$ into the central sequence algebra of $A$. We also discuss some non-trivial examples of strongly self-absorbing actions.