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arXiv · 2509.19148

Regular ideals, Ideal Intersections and Quotients II

Jonathan H. Brown·Adam H. Fuller·David R. Pitts·Sarah A. Reznikoff
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Abstract

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. regular inclusions with the faithful unique pseudo-expectation property, equivalently, 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.

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Jonathan H. Brown, Adam H. Fuller, David R. Pitts, Sarah A. Reznikoff. 2025-09-23. Regular ideals, Ideal Intersections and Quotients II. https://arxiv.org/abs/2509.19148

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