Multiplicative partial isometries, manageability, and C*-algebraic quantum groupoids
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866912921380978688 |
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| author | Kahng, Byung-Jay |
| author_facet | Kahng, Byung-Jay |
| contents | Generalizing the notion of a multiplicative unitary (in the sense of Baaj-Skandalis), which plays a fundamental role in the theory of locally compact quantum groups, we develop in this paper the notion of a multiplicative partial isometry. The axioms include the pentagon equation, but more is needed. Under suitable conditions (such as the "manageability"), it is possible to construct from it a pair of C*-algebras having the structure of a C*-algebraic quantum groupoid of separable type.
Generalizing the notion of a multiplicative unitary operator, which plays a fundamental role in the theory of locally compact quantum groups, we develop in this paper the notion of a multiplicative partial isometry. The axioms include the pentagon equation, but more is needed. Under the "manageability" condition on a multiplicative partial isometry (modified from the Woronowicz's condition for a multiplicative unitary), it is possible to construct from it a pair of C*-algebras having almost the structure of a C*-algebraic quantum groupoid of separable type. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2002_01995 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Multiplicative partial isometries, manageability, and C*-algebraic quantum groupoids Kahng, Byung-Jay Operator Algebras Quantum Algebra 46L67, 20G42, 46L51, 16T20, 22A22 Generalizing the notion of a multiplicative unitary (in the sense of Baaj-Skandalis), which plays a fundamental role in the theory of locally compact quantum groups, we develop in this paper the notion of a multiplicative partial isometry. The axioms include the pentagon equation, but more is needed. Under suitable conditions (such as the "manageability"), it is possible to construct from it a pair of C*-algebras having the structure of a C*-algebraic quantum groupoid of separable type. Generalizing the notion of a multiplicative unitary operator, which plays a fundamental role in the theory of locally compact quantum groups, we develop in this paper the notion of a multiplicative partial isometry. The axioms include the pentagon equation, but more is needed. Under the "manageability" condition on a multiplicative partial isometry (modified from the Woronowicz's condition for a multiplicative unitary), it is possible to construct from it a pair of C*-algebras having almost the structure of a C*-algebraic quantum groupoid of separable type. |
| title | Multiplicative partial isometries, manageability, and C*-algebraic quantum groupoids |
| topic | Operator Algebras Quantum Algebra 46L67, 20G42, 46L51, 16T20, 22A22 |
| url | https://arxiv.org/abs/2002.01995 |