Vol. 273, No. 1, 2015

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Fréchet quantum supergroups

Axel de Goursac

Vol. 273 (2015), No. 1, 169–195
Abstract

We introduce Fréchet quantum supergroups and their representations. By using the universal deformation formula of the abelian supergroups mn we construct various classes of Fréchet quantum supergroups that are deformation of classical ones. For such quantum supergroups, we find an analog of Kac–Takesaki operators that are superunitary and satisfy the pentagonal relation.

Keywords
Hopf algebra, quantum group, noncommutative supergeometry, Fréchet spaces, deformation quantization, multiplicative unitary
Mathematical Subject Classification 2010
Primary: 16T05, 46E10
Secondary: 46L65, 58A50
Milestones
Received: 10 December 2013
Revised: 7 April 2014
Accepted: 8 April 2014
Published: 6 December 2014
Authors
Axel de Goursac
Chargé de Recherches au FRS-FNRS, IRMP
Université Catholique de Louvain
Chemin du Cyclotron 2
1348 Louvain-la-Neuve
Belgium