Regular irreducible inclusions of simple $C^*$-algebras and crossed product structure
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918497764769792 |
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| author | Bakshi, Keshab Chandra C, Silambarasan Pal, Biplab |
| author_facet | Bakshi, Keshab Chandra C, Silambarasan Pal, Biplab |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12221 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Regular irreducible inclusions of simple $C^*$-algebras and crossed product structure Bakshi, Keshab Chandra C, Silambarasan Pal, Biplab Operator Algebras Functional Analysis 46L37, 47L40, 46L05, 43A30 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. |
| title | Regular irreducible inclusions of simple $C^*$-algebras and crossed product structure |
| topic | Operator Algebras Functional Analysis 46L37, 47L40, 46L05, 43A30 |
| url | https://arxiv.org/abs/2605.12221 |