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 - 2015

Y1 - 2015

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 $\mathcal O_\infty$-absorbing C*-algebra and its $\mathcal O_2$-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 $\mathcal O_\infty$-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 $\mathcal O_\infty$-absorbing C*-algebra and its $\mathcal O_2$-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 $\mathcal O_\infty$-absorbing C*-algebras that turn out to have finite nuclear dimension

U2 - 10.4171/JNCG/226

DO - 10.4171/JNCG/226

M3 - Journal article

VL - 9

SP - 1383

EP - 1393

JO - Journal of Noncommutative Geometry

JF - Journal of Noncommutative Geometry

SN - 1661-6952

IS - 4

ER -