Intermediate C∗-algebras of Cartan Embeddings

Authors

Jonathan H. Brown, University of DaytonFollow
Ruy Exel, Universidade Federal de Santa CatarinaFollow
Adam H. Fuller, Ohio UniversityFollow
David R. Pitts, University of Nebraska-LincolnFollow
Sarah A. Reznikoff, Kansas State UniversityFollow

Document Type

Article

Date of this Version

12-10-2019

Citation

arXiv:1912.03686v2 [math.OA] 10 Dec 2019

doi: 10.48550/arXiv.1912.03686
doi: 10.1090/bproc/169

Comments

Copyright © 2019 Jonathan H. Brown, Ruy Exel, Adam H. Fuller, David R. Pitts, and Sarah A. Reznikoff

Abstract

Let A be a C*-algebra and let D be a Cartan subalgebra of A. We study the following question: if B is a C*-algebra such that D B A, is D a Cartan subalgebra of B? We give a positive answer in two cases: the case when there is a faithful conditional expectation from A onto B, and the case when A is nuclear and D is a C*-diagonal of A. In both cases there is a one-to-one correspondence between the intermediate C*-algebras B, and a class of open subgroupoids of the groupoid G, where ! G is the twist associated with the embedding D A.