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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.19148 |
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Table of Contents:
- We continue the study of regular ideals in regular inclusions of C*-algebras. Let $B \subseteq A$ be a regular inclusion of C*-algebras satisfying the ideal intersection property and with a faithful invariant pseudo-expectation. A complete description of the regular ideals of $A$ is given using the invariant regular ideals of $B$ and the pseudo-expectation. Further, necessary and sufficient conditions are given for a quotient by a regular ideal to preserve the faithful unique pseudo-expectation property. Special attention is given throughout to pseudo-Cartan inclusions, i.e. inclusions having a Cartan envelope. We show that the quotient of a pseudo-Cartan inclusion by a regular ideal is again a pseudo-Cartan inclusion, and we describe the Cartan envelope of the quotient.