Multiplicative partial isometries, manageability, and C*-algebraic quantum groupoids

Fuente: arXiv
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Main Author: Kahng, Byung-Jay
Format: Preprint
Published: 2020
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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
id 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