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تسجيل مستخدم جديدLocalizing the Elliott Conjecture at Strongly Self-absorbing C*-algebras --An Appendix
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Huaxin Lin
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This note provides some technical support to the proof of a result of W. Winter which shows that two unital separable simple amenable ${cal Z}$-absorbing C*-algebras with locally finite decomposition property satisfying the UCT whose projections separate the traces are isomorphic if their $K$-theory is finitely generated and their Elliott invariants are the same.
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In this paper, we accomplish two objectives. Firstly, we extend and improve some results in the theory of (semi-)strongly self-absorbing C*-dynamical systems, which was introduced and studied in previous work. In particular, this concerns the theory
when restricted to the case where all the semi-strongly self-absorbing actions are assumed to be unitarily regular, which is a mild technical condition. The central result in the first part is a strengthened version of the equivariant McDuff-type theorem, where equivariant tensorial absorption can be achieved with respect to so-called very strong cocycle conjugacy. Secondly, we establish completely new results within the theory. This mainly concerns how equivariantly $cal Z$-stable absorption can be reduced to equivariantly UHF-stable absorption with respect to a given semi-strongly self-absorbing action. Combining these abstract results with known uniqueness theorems due to Matui and Izumi-Matui, we obtain the following main result. If $G$ is a torsion-free abelian group and $cal D$ is one of the known strongly self-absorbing C*-algebras, then strongly outer $G$-actions on $cal D$ are unique up to (very strong) cocycle conjugacy. This is new even for $mathbb{Z}^3$-actions on the Jiang-Su algebra.
In this paper we consider a bootstrap class $mathfrak C$ of countable discrete groups, which is closed under countable unions and extensions by the integers, and we study actions of such groups on C*-algebras. This class includes all torsion-free abe
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In recent work, Cuntz, Deninger and Laca have studied the Toeplitz type C*-algebra associated to the affine monoid of algebraic integers in a number field, under a time evolution determined by the absolute norm. The KMS equilibrium states of their sy
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