Symmetries of the C*-algebra of a vector bundle

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:494

Article

Deaconu, Valentin¹ 

[1] Univ Nevada, Dept Math & Stat, Reno, NV 89557 USA

关键词: Vector bundle;    C*-correspondence;    Group action;    Continuous fields;    Morita-Rieffel equivalence;    Cuntz-Pimsner algebra;   

DOI  :  10.1016/j.jmaa.2020.124607

来源: Elsevier

【 摘 要 】

We consider C*-algebras constructed from compact group actions on complex vector bundles E -> Xendowed with a Hermitian metric. An action of Gby isometries on E -> Xinduces an action on the C*-correspondence Gamma(E) over C(X) consisting of continuous sections, and on the associated Cuntz-Pimsner algebra O-E, so we can study the crossed product O-E x G. If the action is free and rank E=n, then we prove that O-E x G is Morita-Rieffel equivalent to a field of Cuntz algebras O-n over the orbit space X/G. If the action is fiberwise, then O-E x G becomes a continuous field of crossed products O-n x G. For transitive actions, we show that O-E x G is Morita-Rieffel equivalent to a graph C*-algebra. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free