Crossed products by finite group actions with the Rokhlin property
نویسندگان
چکیده
منابع مشابه
Crossed Products by Finite Group Actions with the Rokhlin Property
We prove that a number of classes of separable unital C*-algebras are closed under crossed products by finite group actions with the Rokhlin property, including: • AI algebras, AT algebras, and related classes characterized by direct limit decompositions using semiprojective building blocks. • Simple unital AH algebras with slow dimension growth and real rank zero. • C*-algebras with real rank ...
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We define the tracial Rokhlin property for actions of finite cyclic groups on stably finite simple unital C*-algebras. We prove that the crossed product of a stably finite simple unital C*-algebra with tracial rank zero by an action with this property again has tracial rank zero. Under a kind of weak approximate innerness assumption and one other technical condition, we prove that if the action...
متن کاملFinite Cyclic Group Actions with the Tracial Rokhlin Property
We give examples of actions of Z/2Z on AF algebras and AT algebras which demonstrate the differences between the (strict) Rokhlin property and the tracial Rokhlin property, and between (strict) approximate representability and tracial approximate representability. Specific results include the following. We determine exactly when a product type action of Z/2Z on a UHF algebra has the tracial Rok...
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and Applied Analysis 3 Lemma 2.2 see 5, Theorem 3.3 , 6, Theorem 3.3 . Let A be a simple unital C∗-algebra. If TRR A 0, then RR A 0. If Tsr A 1 and has the (SP)-property, then tsr A 1. Definition 2.3 see 13, Definition 1.2 . Let A be an infinite dimensional finite simple separable unital C∗-algebra, and let α : G → Aut A be an action of a finite group G on A. We say that α has the tracial Rokhl...
متن کاملStable and Real Rank for Crossed Products by Automorphisms with the Tracial Rokhlin Property
We introduce the tracial Rokhlin property for automorphisms of stably finite simple unital C*-algebras containing enough projections. This property is formally weaker than the various Rokhlin properties considered by Herman and Ocneanu, Kishimoto, and Izumi. Our main results are as follows. Let A be a stably finite simple unital C*-algebra, and let α be an automorphism of A which has the tracia...
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2011
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-010-0784-4