Rokhlin actions and self-absorbing C*-algebras

By Ilan Hirshberg, W. Winter. 2005

83 citations recorded by the source corpus.

Let A be a unital separable C∗-algebra, and D a K1-injective strongly selfabsorbing C∗-algebra. We show that if A is D-absorbing, then the crossed product of A by a compact second countable group or by Z or by R is D-absorbing as well, assuming the action satisfying a Rokhlin property. In the case of a compact Rokhlin action we prove a similar statement about approximate divisibility.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/90d78d17854fdd5718747dcb02c4f8b1f29abd36

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Citations in the corpus

The Rohlin property for automorphisms of the Jiang-Su algebra (2009, methodology): “itions for ﬁnite actions, which is called projection free tracial Rohlin property, has been deﬁned in [1], [25]. The ﬁrst main theorem is an adaptation of the result showed by Hirshberg and Winter in [12] to projectionless C∗-algebras. The second main theorem is an adaptation of the result for UHF a”
Rokhlin dimension for compact group actions (2014, methodology): “3 of [14] is unnecessary: its kernel is a translation-invariant ideal of C(G), so it must be either {0} or C(G).”
Rokhlin dimension for actions of residually finite groups (2014, background): “For a selection of other papers related to Rokhlin-type properties for C-dynamical systems, see [6, 18, 27, 43, 48, 50, 52, 55, 58, 59, 64, 65] (this list is not exhaustive).”
Sequentially split ∗-homomorphisms between C*-algebras (2015, background): “this situation, the universal properties yield that the induced ∗-homomorphism ϕ⋊P : A⋊αP → B⋊βP is also sequentially split. 4. Applications 4.1. Rokhlin actions of compact groups. Deﬁnition 4.1 (cf. [23]). Let Abe a separable C∗-algebra and Ga second countable, compact group. Let σ: GyC(G) denote t”
Rokhlin Dimension and C*-Dynamics (2012, methodology): “1) = 1, and those two order zero maps satisfy the conditions of Corollary 5.5. Therefore Ao Gis Z-stable, as required. The main theorem of this section is a partial generalization of Theorem 4.4 from [8] (that theorem is for the Rokhlin property, but it applies to absorption of general strongly self”
Freeness of actions of finite groups on C*-algebras (2009, background): “See [23] for the definition of a strongly self-absorbing C*-algebra.”
Strongly self-absorbing C*-algebras (2005, methodology): “ents, inductive limits and to extensions. In the cases where D equals O 2 or O∞ these results were obtained independently (and with slightly diﬀerent methods) by E. Kirchberg, cf. [20], Section 8. In [14], I. Hirshberg and the second named author will show that D-stability also passes to crossed pro”
Strongly self-absorbing C*-algebras are Z-stable (2009, background): “3 Remark: By [9], Z-stable C-algebras are K1-injective, whence K1-injectivity is unnecessary in the hypotheses of the main results of [12], [2], [3], [5], [6] and [7].”
Localizing the Elliott conjecture at strongly self-absorbing C*-algebras (2007, background): “…products with generalized dimension drop intervals and show how such an isomorphism may be used to obtain an asymptotic unitary intertwining between tensor products with Z. 4.1 Notation: For 0 m ≤ n ∈ N and unital C∗-algebrasA1, . . . , Am, B1, . . . , Bn let i1, . . . , im ∈ {1, . . . , n be…”
C_0(X)-algebras, stability and strongly self-absorbing C*-algebras (2006, background): “D-stability does not pass in general to crossed products; however, it does pass to crossed products by Z, R or by compact groups provided the group action has a Rokhlin property ([13]).”