Weak quantum hypergroups from finite index C*-inclusions
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911383855038464 |
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| author | Bakshi, Keshab Chandra Goswami, Debashish Pal, Biplab |
| author_facet | Bakshi, Keshab Chandra Goswami, Debashish Pal, Biplab |
| contents | We study a finite index inclusion of simple unital C*-algebras and construct a canonical completely positive coproduct on the second relative commutant, thereby endowing it with a natural coalgebra structure. Motivated by this construction, we introduce the notion of a weak quantum hypergroup, a generalization of the quantum hypergroups of Chapovsky and Vainerman. We show that every finite index inclusion gives rise to such a weak quantum hypergroup, and that the corresponding weak quantum hypergroup possesses a Haar integral. In the irreducible case, this structure satisfies the axioms of a quantum hypergroup in the sense of Chapovsky and Vainerman, while in the depth 2 setting our framework yields the associated weak Hopf algebra constructed by Nikshych and Vainerman. These results provide a unified and intrinsically C*-algebraic framework for generalized quantum symmetries associated with finite index inclusions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12406 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weak quantum hypergroups from finite index C*-inclusions Bakshi, Keshab Chandra Goswami, Debashish Pal, Biplab Operator Algebras Functional Analysis We study a finite index inclusion of simple unital C*-algebras and construct a canonical completely positive coproduct on the second relative commutant, thereby endowing it with a natural coalgebra structure. Motivated by this construction, we introduce the notion of a weak quantum hypergroup, a generalization of the quantum hypergroups of Chapovsky and Vainerman. We show that every finite index inclusion gives rise to such a weak quantum hypergroup, and that the corresponding weak quantum hypergroup possesses a Haar integral. In the irreducible case, this structure satisfies the axioms of a quantum hypergroup in the sense of Chapovsky and Vainerman, while in the depth 2 setting our framework yields the associated weak Hopf algebra constructed by Nikshych and Vainerman. These results provide a unified and intrinsically C*-algebraic framework for generalized quantum symmetries associated with finite index inclusions. |
| title | Weak quantum hypergroups from finite index C*-inclusions |
| topic | Operator Algebras Functional Analysis |
| url | https://arxiv.org/abs/2601.12406 |