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18
FREENESS OF ACTIONS OF FINITE GROUPS ON C*ALGEBRAS
, 2009
"... We describe some of the forms of freeness of group actions on noncommutative C*algebras that have been used, with emphasis on actions of finite groups. We give some indications of their strengths, weaknesses, applications, and relationships to each other. The properties discussed include the Rokh ..."
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We describe some of the forms of freeness of group actions on noncommutative C*algebras that have been used, with emphasis on actions of finite groups. We give some indications of their strengths, weaknesses, applications, and relationships to each other. The properties discussed include the Rokhlin property, Ktheoretic freeness, the tracial Rokhlin property, pointwise outerness, saturation, hereditary saturation, and the requirement that the strong Connes spectrum be the entire dual.
Permanence properties for crossed products and fixed point algebras of finite groups
 Trans. Amer. Math. Soc
"... Abstract. Let α: G → Aut(A) be an action of a finite group G on a C*algebra A. We present some conditions under which properties of A pass to the crossed product C∗(G,A, α) or the fixed point algebra Aα. We mostly consider the ideal property, the projection property, topological dimension zero, and ..."
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Abstract. Let α: G → Aut(A) be an action of a finite group G on a C*algebra A. We present some conditions under which properties of A pass to the crossed product C∗(G,A, α) or the fixed point algebra Aα. We mostly consider the ideal property, the projection property, topological dimension zero, and pure infiniteness. In many of our results, additional conditions are necessary on the group, the algebra, or the action. Sometimes the action must be strongly pointwise outer, and in a few results it must have the Rokhlin property. When G is finite abelian, we prove that crossed products and fixed point algebras by G preserve topological dimension zero with no condition on the action. We give an example to show that the ideal property and the projection property do not pass to fixed point algebras (even when the group is Z2). The construction also gives an example of a C*algebra B which does not have the ideal property but such that M2(B) does have the ideal property; in fact, M2(B) has the projection property.
Compact group actions with the Rokhlin property and their crossed products
, 2014
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NONSIMPLE TRACIAL APPROXIMATION QINGZHAI FAN AND XIAOCHUN FANG
"... Abstract. We show that the following properties of C∗algebras in the class Ω are inherited by C∗algebras in the class TAΩ: (1) K1surjective property, (2) K1injective property, (3) Stable weak cancelation property, (4) Stable finite property, (5) Having at least one tracial state. 1. ..."
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Abstract. We show that the following properties of C∗algebras in the class Ω are inherited by C∗algebras in the class TAΩ: (1) K1surjective property, (2) K1injective property, (3) Stable weak cancelation property, (4) Stable finite property, (5) Having at least one tracial state. 1.
THE KTHEORY OF A SIMPLE SEPARABLE EXACT C*ALGEBRA NOT ISOMORPHIC TO ITS OPPOSITE ALGEBRA
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