Mathematics, Department of
Department of Mathematics: Faculty Publications
Accessibility Remediation
If you are unable to use this item in its current form due to accessibility barriers, you may request remediation through our remediation request form.
Document Type
Article
Date of this Version
12-15-2023
Citation
Integr. Equ. Oper. Theory (2024) 96:3 https://doi.org/10.1007/s00020-023-02753-4
Abstract
Let B ⊆ A be an inclusion of C∗ -algebras. We study the relationship between the regular ideals of B and regular ideals of A.We show that if B ⊆ A is a regular C∗ -inclusion and there is a faithful invariant conditional expectation from A onto B, then there is an isomorphism between the lattice of regular ideals of A and invariant regular ideals of B. We study properties of inclusions preserved under quotients by regular ideals. This includes showing that if D ⊆ A is a Cartan inclusion and J is a regular ideal in A, then D/(J ∩D) is a Cartan subalgebra of A/J. We provide a description of regular ideals in the reduced crossed product of a C∗ -algebra by a discrete group.
Comments
Open access.