The Rokhlin property vs. Rokhlin dimension 1 on unital Kirchberg algebras.
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The Rokhlin property vs. Rokhlin dimension 1 on unital Kirchberg algebras. / Barlak, S.; Enders, Dominic; Matui, H.; Szabo, G.; Winter, W.
I: Journal of Noncommutative Geometry, Bind 9, Nr. 4, 2015, s. 1383–1393.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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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 -
ID: 138511461