Topological freeness for C*-correspondences

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:473

Article

Carlsen, Toke Meier¹  Kwasniewski, Bartosz Kosma²  Ortega, Eduard³ 

[1] Univ Faroe Isl, Dept Sci & Technol, Vestara Bryggja 15, FO-100 Torshavn, Denmark

[2] Univ Bialystok, Inst Math, Ul K Ciolkowskiego 1M, PL-15245 Bialystok, Poland

[3] NTNU, Dept Math Sci, NO-7491 Trondheim, Norway

关键词: Topological freeness;    C*-correspondence;    Cuntz-Pimsner algebra;   

DOI  :  10.1016/j.jmaa.2018.12.069

来源: Elsevier

【 摘 要 】

We study conditions that ensure uniqueness theorems of Cuntz-Krieger type for relative Cuntz-Pimsner algebras O(J, X) associated to a C*-correspondence X over a C*-algebra A. We give general sufficient conditions phrased in terms of a multivalued map (X) over cap acting on the spectrum (A) over cap of A. When X (J). is of Type I we construct a directed graph dual to X and prove a uniqueness theorem using this graph. When X(J) is liminal, we show that topological freeness of this graph is equivalent to the uniqueness property for O(J, X), as well as to an algebraic condition which we call J-acyclicity of X. As an application we improve the Fowler-Raeburn uniqueness theorem for the Toeplitz algebra T-X. We give new simplicity criteria for O-X. We generalize and enhance uniqueness results for relative quiver C*-algebras of Muhly and Tomforde. We also discuss applications to crossed products by endomorphisms. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free