Fr\'echet Quantum Supergroups

TL;DR

This paper introduces Fréchet quantum supergroups, constructs their deformations from classical supergroups using universal deformation formulas, and identifies superunitary operators satisfying key algebraic relations.

Contribution

It presents the first construction of Fréchet quantum supergroups and develops their representation theory with superunitary operators.

Findings

Constructed various classes of Fréchet quantum supergroups.

Identified superunitary Kac-Takesaki operators satisfying pentagonal relations.

Established analogs of classical structures in the quantum supergroup setting.

Abstract

In this paper, we introduce Fr\'echet quantum supergroups and their representations. By using the universal deformation formula of the abelian supergroups R^{m|n} we construct various classes of Fr\'echet 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.