The Rohlin property for automorphisms of the Jiang-Su algebra

By Yasuhiko Sato. 2009

71 citations recorded by the source corpus.

For projectionless C*-algebras absorbing the Jiang-Su algebra tensorially, we study a kind of the Rohlin property for autmorphisms. We show that the crossed products obtained by automorphisms with this Rohlin property also absorb the Jiang-Su algebra tensorially under a mild technical condition on the C*-algebras. In particular, for the Jiang-Su algebra we show the uniqueness up to outer conjugacy of the automorphism with this Rohlin property.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/30fcf956c9a49b8b5dc18c69803b207855e1169b

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In Algebra and Number Theory

1. G'abor Szab'o
2. W. Winter
3. Ilan Hirshberg
4. H. Matui
5. J. Zacharias
6. Yasuhiko Sato
7. Jianchao Wu
8. Joav Orovitz

In Geometry and Topology

1. G'abor Szab'o
2. J. Zacharias
3. H. Matui
4. Yasuhiko Sato
5. Ilan Hirshberg
6. Jianchao Wu
7. Joav Orovitz
8. W. Winter

In Mathematical Physics

1. G'abor Szab'o
2. W. Winter
3. Yasuhiko Sato
4. J. Zacharias
5. David Kerr
6. Ilan Hirshberg
7. H. Matui
8. Jianchao Wu

Citations in the corpus

• Tracially Z-absorbing C*-algebras (2012, background): “Further tracial-type generalizations in which the projections are replaced by positive elements were considered in [21, 1], and we will study a closely related variant.”
• Equivariant Kirchberg–Phillips-Type Absorption for Amenable Group Actions (2016, background): “The only obvious exception is Matui-Sato’s weak Rokhlin property [54, 55] originating in [69].”
• Rokhlin Dimension and C*-Dynamics (2012, background): “We note that other generalizations of the Rokhlin property have been considered which are based on the idea of leaving out a remainder which is small in the tracial sense (see [19, 25, 1, 6, 22]).”
• Strict comparison and $$ \mathcal{Z} $$-absorption of nuclear C∗-algebras (2011, methodology): “2 (i) in [20], we may assume lim n max τ dτ (en) = 0.”
• Strict comparison and Z-absorption of nuclear C*-algebras (2011, methodology): “1. Then for any norm one positive element a∈ A, there exists a sequence (rn)n in Asuch that lim n→∞ kr∗ nf 1/2 n af 1/2 n rn −enk = 0, limsup n→∞ krnk = limsup n→∞ kenk1/2. Proof. By Lemma 3.2 (i) in [19], we may assume lim n max τ dτ(en) = 0. Set c= lim m→∞ liminf n→∞ min τ∈T(A) τ(fm n ) >0. Tak”
• Rokhlin dimension for actions of residually finite groups (2014, background): “For a selection of other papers related to Rokhlin-type properties for C-dynamical systems, see [6, 18, 27, 43, 48, 50, 52, 55, 58, 59, 64, 65] (this list is not exhaustive).”