Fréchet quantum supergroups

Axel de Goursac

Vol. 273 (2015), No. 1, 169–195

DOI: 10.2140/pjm.2015.273.169

Abstract

We introduce Fréchet quantum supergroups and their representations. By using the universal deformation formula of the abelian supergroups ${ℝ}^{m\mid n}$ 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