On the von Neumann algebra of class functions on a compact quantum group

Autor:	Mateusz Wasilewski, Jacek Krajczok
Rok vydání:	2022
Předmět:	Mathematics::Operator Algebras Mathematics::Quantum Algebra Mathematics - Quantum Algebra FOS: Mathematics Mathematics - Operator Algebras Quantum Algebra (math.QA) Operator Algebras (math.OA) 46L67 (Primary) 20G42 (Secondary) Analysis
Zdroj:	Journal of Functional Analysis. 283:109549
ISSN:	0022-1236
Popis:	We study analogues of the radial subalgebras in free group factors (called the algebras of class functions) in the setting of compact quantum groups. For the free orthogonal quantum groups we show that they are not MASAs, as soon as we are in a non-Kac situation. The most important notion to our present work is that of a (quasi-)split inclusion. We prove that the inclusion of the algebra of class functions is quasi-split for some unitary quantum groups; in this case the subalgebra is non-abelian and we also obtain a result concerning its relative commutant. In the positive direction, we construct certain bicrossed products from the quantum group $SU_q(2)$ for which the algebra of class functions is a MASA. 20 pages
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b44a12f22503df0a9567288e8296440e https://doi.org/10.1016/j.jfa.2022.109549 Zobrazit plný text záznamu Full Text from ScienceDirect