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arXiv · 2605.12221

Regular irreducible inclusions of simple $C^*$-algebras and crossed product structure

Keshab Chandra Bakshi·Silambarasan C·Biplab Pal
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Abstract

We study regular irreducible inclusions $B\subset A$ of simple unital $C^*$-algebras admitting a conditional expectation. We introduce a generalized notion of quasi-basis extending Watatani's framework and show that such inclusions admit a unitary orthonormal generalized quasi-basis. As a consequence, we prove that every regular irreducible inclusion in this setting is canonically isomorphic to a reduced twisted crossed product of $B$ by its Weyl group. This extends earlier crossed product characterizations beyond the finite-index setting.

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Keshab Chandra Bakshi, Silambarasan C, Biplab Pal. 2026-05-12. Regular irreducible inclusions of simple $C^*$-algebras and crossed product structure. https://arxiv.org/abs/2605.12221

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