Crossed products by finite group actions with the Rokhlin property
By Hiroyuki Osaka, N. Christopher Phillips. 2007
65 citations recorded by the source corpus.
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: (a) AI algebras, AT algebras, and related classes characterized by direct limit decompositions using semiprojective building blocks. (b) Simple unital AH algebras with slow dimension growth and real rank zero. (c) C*-algebras with real rank zero or stable rank one. (d) Simple C*-algebras for which the order on projections is determined by traces. (e) C*-algebras whose quotients all satisfy the Universal Coefficient Theorem. (f) C*-algebras with a unique tracial state. Along the way, we give a systematic treatment of the derivation of direct limit decompositions from local approximation conditions by homomorphic images which are not necessarily injective.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/fb78725b502244159c4405c173bb8991d42323f0
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In Algebra and Number Theory
- G'abor Szab'o
- Eusebio Gardella
- Ilan Hirshberg
- Jianchao Wu
- J. Zacharias
- Joav Orovitz
- Selccuk Barlak
- W. Winter
In Mathematical Physics
- G'abor Szab'o
- Eusebio Gardella
- Jianchao Wu
- J. Zacharias
- Ilan Hirshberg
- Joav Orovitz
- Selccuk Barlak
- W. Winter
Citations in the corpus
- Rokhlin dimension for compact group actions (2014, background): “See [23] and [18] for integer actions, and see [12], [16], [17] and [26] for the finite group case.”
- Sequentially split ∗-homomorphisms between C*-algebras (2015, background): “The following result arises as an immediate consequence, and generalizes many permanence property results of [44, 55, 27, 20].”
- Tracially Z-absorbing C*-algebras (2012, background): “The Rokhlin property has been instrumental in the study of group actions on C∗-algebras (see [5] for a survey, [6, 7, 16] for the finite group case, [11] and references therein for the single automorphism case).”
- 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).”