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Strongly outer acti...
Strongly outer actions of amenable groups on Z-stable nuclear C*-algebras
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- Gardella, Eusebio (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Chalmers tekniska högskola,Chalmers University of Technology
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- Hirshberg, I. (author)
- Ben-Gurion University of the Negev
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Vaccaro, A. (author)
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(creator_code:org_t)
- Elsevier BV, 2022
- 2022
- English.
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In: Journal des Mathématiques Pures et Appliquées. - : Elsevier BV. - 0021-7824. ; 162, s. 76-123
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Abstract
Subject headings
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- Let A be a separable, unital, simple, Z-stable, nuclear C*-algebra, and let alpha: G -+ Aut(A) be an action of a discrete, countable, amenable group. Suppose that the orbits of the action of G on T(A) are finite and that their cardinality is bounded. We show that the following are equivalent: (1) alpha is strongly outer; (2) alpha (R) idZ has the weak tracial Rokhlin property. If G is moreover residually finite, the above conditions are also equivalent to (3) alpha (R) idZ has finite Rokhlin dimension (in fact, at most 2). If partial differential eT(A) is furthermore compact, has finite covering dimension, and the orbit space partial differential eT(A)/G is Hausdorff, we generalize results by Matui and Sato to show that alpha is cocycle conjugate to alpha (R) idZ, even if alpha is not strongly outer. In particular, in this case the equivalences above hold for alpha in place of alpha (R) idZ. In the course of the proof, we develop equivariant versions of complemented partitions of unity and uniform property Gamma as technical tools of independent interest. (c) 2022 The Author(s). Published by Elsevier Masson SAS. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Algebra och logik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Algebra and Logic (hsv//eng)
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Geometri (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Geometry (hsv//eng)
Keyword
- Group action
- Amenability
- Jiang-Su algebra
- Strong outerness
- tracial rokhlin property
- finite-group actions
- crossed-products
- rohlin
- property
- model-theory
- z-stability
- automorphisms
- dimension
- Mathematics
- Amenability
Publication and Content Type
- ref (subject category)
- art (subject category)
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