## Mathematics, Department of

#### Date of this Version

12-10-2019

#### Citation

2019 Authors

#### 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.

## Comments

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