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• W3210149621 abstract "We define a analog of the Rokhlin property for actions of second countable compact groups on infinite dimensional simple separable unital C*-algebras. We prove that fixed point algebras under such actions (and, in the appropriate cases, crossed products by such actions) preserve simplicity, Property (SP), tracial rank zero, the Popa property, and pure infiniteness. Our version of the tracial Rokhlin property is an exact generalization of the tracial Rokhlin property for actions of finite groups on classifiable C*-algebras (in the sense of the Elliott program), but for actions of finite groups on more general C*-algebras it may be stronger. We discuss several alternative versions of the tracial Rokhlin property. We give examples of actions of a totally disconnected infinite compact group on a UHF algebra, and of the circle group on a simple unital AT algebra, which have our version of the tracial Rokhlin property, but do not have the Rokhlin property, or even finite Rokhlin dimension with commuting towers." @default.
• W3210149621 created "2021-11-08" @default.
• W3210149621 creator A5071473075 @default.
• W3210149621 creator A5091215062 @default.
• W3210149621 date "2021-10-23" @default.
• W3210149621 modified "2023-09-27" @default.
• W3210149621 title "Compact Group Actions with the Tracial Rokhlin Property" @default.
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• W3210149621 hasPublicationYear "2021" @default.
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