The Rokhlin property for endomorphisms and strongly self-absorbing $C^{*}$-algebras
نویسندگان
چکیده
منابع مشابه
Rokhlin Actions and Self-absorbing C∗-algebras
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.
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Say that a separable, unital C *-algebra D ≇ C is strongly self-absorbing if there exists an isomorphism ϕ : D → D ⊗ D such that ϕ and id D ⊗ 1 D are approximately unitarily equivalent *-homomorphisms. We study this class of algebras, which includes the Cuntz algebras O 2 , O∞, the UHF algebras of infinite type, the Jiang–Su algebra Z and tensor products of O∞ with UHF algebras of infinite type...
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Let A be a unital separable C∗-algebra, and D a strongly selfabsorbing C∗-algebra (in the sense of Toms and Winter). We show that if A is D-absorbing, then the crossed product of A by a finite group is D-absorbing as well, assuming the action satisfying a Rokhlin property. With some extra restrictions on A and D, we obtain a similar result for crossed products by Z.
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Let D and A be unital and separable C∗-algebras; let D be strongly selfabsorbing. It is known that any two unital ∗-homomorphisms from D to A ⊗ D are approximately unitarily equivalent. We show that, if D is also K1-injective, they are even asymptotically unitarily equivalent. This in particular implies that any unital endomorphism of D is asymptotically inner. Moreover, the space of automorphi...
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We study a general Kishimoto’s problem for automorphisms on simple C∗-algebras with tracial rank zero. Let A be a unital separable simple C∗-algebra with tracial rank zero and let α be an automorphism. Under the assumption that α has certain Rokhlin property, we present a proof that A ⋊α Z has tracial rank zero. We also show that if the induced map α∗0 on K0(A) fixes a “dense” subgroup of K0(A)...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 2014
ISSN: 0019-2082
DOI: 10.1215/ijm/1441790380