The Rokhlin property vs. Rokhlin dimension 1 on unital Kirchberg algebras.

TY - JOUR

T1 - The Rokhlin property vs. Rokhlin dimension 1 on unital Kirchberg algebras.

AU - Barlak, S.

AU - Enders, Dominic

AU - Matui, H.

AU - Szabo, G.

AU - Winter, W.

PY - 2016

Y1 - 2016

N2 - We investigate outer symmetries on unital Kirchberg algebras with respect to the Rokhlin property and finite Rokhlin dimension. In stark contrast to the restrictiveness of the Rokhlin property, every such action has Rokhlin dimension at most one. A consequence of these observations is a relationship between the nuclear dimension of an O∞-absorbing C∗-algebra and its O2-stabilization. We also give a more direct and alternative approach to this result. Several applications of this relationship are discussed to cover a fairly large class of O∞-absorbing C∗-algebras that turn out to have finite nuclear dimension.

AB - We investigate outer symmetries on unital Kirchberg algebras with respect to the Rokhlin property and finite Rokhlin dimension. In stark contrast to the restrictiveness of the Rokhlin property, every such action has Rokhlin dimension at most one. A consequence of these observations is a relationship between the nuclear dimension of an O∞-absorbing C∗-algebra and its O2-stabilization. We also give a more direct and alternative approach to this result. Several applications of this relationship are discussed to cover a fairly large class of O∞-absorbing C∗-algebras that turn out to have finite nuclear dimension.

U2 - 10.4171/jncg/226

DO - 10.4171/jncg/226

M3 - Journal article

SN - 1661-6952

VL - 9

SP - 1383

EP - 1393

JO - Journal of Noncommutative Geometry

JF - Journal of Noncommutative Geometry

IS - 4

ER -