Strongly self-absorbing 𝐶*-dynamical systems

Abstract

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