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dc.contributor.authorTuset, Lars
dc.contributor.authorBieliavsky, Pierre
dc.contributor.authorGayral, Victor
dc.contributor.authorNeshveyev, Sergey
dc.identifier.citationTuset, L., Bieliavsky, P., Gayral, V. & Neshveyev, S. (2021). Quantization of subgroups of the affine group. Journal of Functional Analysis, 280(4), 108844. doi:
dc.description.abstractConsider a locally compact group such that V is abelian and the action of Q on the dual abelian group has a free orbit of full measure. We show that such a group G can be quantized in three equivalent ways: (1) by reflecting across the Galois object defined by the canonical irreducible representation of G on ; (2) by twisting the coproduct on the group von Neumann algebra of G by a dual 2-cocycle obtained from the G-equivariant Kohn–Nirenberg quantization of ; (3) by considering the bicrossed product defined by a matched pair of subgroups of both isomorphic to Q. In the simplest case of the group over the reals, the dual cocycle in (2) is an analytic analogue of the Jordanian twist. It was first found by Stachura using different ideas. The equivalence of approaches (2) and (3) in this case implies that the quantum group of Baaj–Skandalis is isomorphic to the quantum group defined by Stachura. Along the way we prove a number of results for arbitrary locally compact groups G. Using recent results of De Commer we show that a class of G-Galois objects is parametrized by certain cohomology classes in . This extends results of Wassermann and Davydov in the finite group case. A new phenomenon is that already the unit class in can correspond to a nontrivial Galois object. Specifically, we show that any nontrivial locally compact group G with group von Neumann algebra a factor of type I admits a canonical cohomology class of dual 2-cocycles such that the corresponding quantization of G is neither commutative nor cocommutative.en
dc.relation.ispartofseriesJournal of Functional Analysis;Volume 280, Issue 4, 108844
dc.rightsCreative Commons Attribution 4.0 International (CC BY 4.0) Licenseen
dc.subjectQuantum groupsen
dc.subjectDual cocyclesen
dc.subjectKohn-Nirenberg quantizationsen
dc.subjectVDP::Matematikk og Naturvitenskap: 400::Matematikk: 410::Algebra/algebraisk analyse: 414en
dc.titleQuantization of subgroups of the affine groupen
dc.typeJournal articleen
dc.typePeer revieweden
dc.source.journalJournal of Functional Analysis

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Creative Commons Attribution 4.0 International (CC BY 4.0) License
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