Strongly self-absorbing *-dynamical systems
By G'abor Szab'o. 2015
61 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ee9a7ecbf79a3ded80d0677e92e0acbbf529a13b
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In Algebra and Number Theory
In Mathematical Physics
Citations in the corpus
- Equivariant Kirchberg–Phillips-Type Absorption for Amenable Group Actions (2016, background): “Although little evidence for this could be given in the initial theory-building work carried out in [72,76], the most recent [75] of these articles allowed for a small breakthrough concerning the uniqueness of strongly outer actions on strongly self-absorbing C∗-algebras, which is now verified for t”
- Sequentially split ∗-homomorphisms between C*-algebras (2015, background): “nt to an isomorphism µ, that is, there exists a sequence un∈ U(D⊗D) such that µ= limn→∞ Ad(un)◦(idD ⊗1D) and limn→∞ k(γ⊗γ)g(un)−unk = 0 uniformly on compact subsets of G. Combining the main result of [59] with 4.2, we see that equivariant tensorial absorption of a strongly self-absorbing action can ”