The Rohlin property for automorphisms of the Jiang-Su algebra
Yasuhiko Sato
TL;DR
This paper investigates a specific Rohlin property for automorphisms of the Jiang-Su algebra, demonstrating that such automorphisms produce crossed products that also absorb the Jiang-Su algebra, and establishing uniqueness up to outer conjugacy.
Contribution
It introduces a Rohlin property for automorphisms of Jiang-Su algebra absorbing C*-algebras and proves the resulting crossed products retain Jiang-Su absorption and automorphism uniqueness.
Findings
Crossed products with Rohlin automorphisms absorb Jiang-Su algebra
Uniqueness of Rohlin automorphisms up to outer conjugacy
Mild technical conditions ensure preservation of properties
Abstract
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.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Algebraic structures and combinatorial models