Strongly self-absorbing 𝐶*-dynamical systems

Szabó, Gábor

doi:10.1090/tran/6931

Strongly self-absorbing $\mathrm {C}^*$-dynamical systems
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by Gábor Szabó PDF

Trans. Amer. Math. Soc. 370 (2018), 99-130 Request permission

Corrigendum: Trans. Amer. Math. Soc. 373 (2020), 7527-7531.

Abstract:

We introduce and study strongly self-absorbing actions of locally compact groups on $\mathrm {C}^*$-algebras. This is an equivariant generalization of a strongly self-absorbing $\mathrm {C}^*$-algebra to the setting of $\mathrm {C}^*$-dynamical systems. The main result is the following equivariant McDuff-type absorption theorem: A cocycle action $(\alpha ,u): G\curvearrowright A$ on a separable $\mathrm {C}^*$-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.

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