Strongly self-absorbing C*-dynamical systems

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 $\ast$-homomorphism from $\mathcal{D}$ into the central sequence algebra of $A$. We also discuss some non-trivial examples of strongly self-absorbing actions.

v2 32 pages; this revision fixes a mistake that made it into the published version. The main results are unchanged, but some intermediate proofs are modified if they previously referred to (the false) "Corollary 1.16" in the previous version

References in corpus (7)

• Strongly self-absorbing C*-algebras are Z-stable
• The nuclear dimension of C*-algebras
• The spatial Rokhlin property for actions of compact quantum groups
• Decomposition rank and Z-stability
• Classification of outer actions of Z^N on O_2
• Z^N-actions on UHF algebras of infinite type
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Cited by in corpus (18)

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• On characterizations of amenable C*-dynamical systems and new examples
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• On a categorical framework for classifying C*-dynamics up to cocycle conjugacy
• Actions of certain torsion-free elementary amenable groups on strongly self-absorbing C*-algebras
• Equivariant ${\mathcal{O}}_2$-absorption theorem for exact groups
• The classification of Rokhlin flows on C*-algebras
• Rokhlin dimension: absorption of model actions
• Poly-$\mathbb{Z}$ group actions on Kirchberg algebras II
• Strongly outer actions of amenable groups on $\mathcal{Z}$-stable nuclear $C^{\ast }$-algebras
• Equivariant higher twisted K-theory of SU(n) for exponential functor twists
• Equivariant bundles and absorption
• Rohlin actions of finite groups on the Razak-Jacelon algebra
• Equivariant property Gamma and the tracial local-to-global principle for C*-dynamics
• A classification of anomalous actions through model action absorption
• Quasi-invariant lifts of completely positive maps for groupoid actions
• Equivariant Kirchberg-Phillips type absorption for the Razak-Jacelon algebra