Rokhlin property for group actions on Hilbert \(C^*\)-modules

zbMATH Open1499.46120arXiv1605.06050MaRDI QIDQ2153056

Hiroyuki Osaka, Santanu Dey, Harsh Trivedi

Publication date: 1 July 2022

Published in: Southeast Asian Bulletin of Mathematics (Search for Journal in Brave)

Abstract: We introduce Rokhlin properties for certain discrete group actions on $C^{*}$-correspondences as well as on Hilbert bimodules and analyze them. It turns out that the group actions on any $C^{*}$-correspondence $E$ with Rokhlin property induces group actions on the associated $C^{*}$-algebra $mathcal{O}_E$ with Rokhlin property and the group actions on any Hilbert bimodule with Rokhlin property induces group actions on the linking algebra with Rokhlin property. Permanence properties of several notions such as nuclear dimension and $mathcalD$-absorbing property with respect to crossed product of Hilbert $C^{*}$-modules with groups, where group actions have Rokhlin property, are studied. We also investigate a notion of outerness for Hilbert bimodules.

Full work available at URL: https://arxiv.org/abs/1605.06050

zbMATH Keywords

crossed productsCuntz-Pimsner algebragroup actionnuclear dimensionRokhlin propertyHilbert \(C^*\)-moduleslinking algebrasself-absorbing \(C^*\)-algebras

Mathematics Subject Classification ID

(C^*)-modules (46L08) Noncommutative dynamical systems (46L55) Classifications of (C^*)-algebras (46L35) Automorphisms of selfadjoint operator algebras (46L40)

Related Items (4)

The weak tracial Rokhlin property for finite group actions on simple $C^*$-algebras ⋮ The tracial Rokhlin property for actions of finite groups on C*-algebras ⋮ The spatial Rokhlin property for actions of compact quantum groups ⋮ Crossed products by compact group actions with the Rokhlin property

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