A (p,q) Deformation of the Universal Enveloping Superalgebra U(osp(2/2))

TL;DR

This paper introduces a two-parameter quantum deformation of the universal enveloping superalgebra U(osp(2/2)), extending the Faddeev-Reshetikhin-Takhtajan formalism to supersymmetry, and establishes its Hopf algebra structure.

Contribution

It presents the first two-parameter quantum deformation of U(osp(2/2)) with a detailed Hopf algebra structure in the supersymmetric setting.

Findings

U_{p,q}(osp(2/2)) is a non-commutative, non-cocommutative Hopf algebra.

Results are expressed using quantum Chevalley basis.

Extends formalism to supersymmetric quantum groups.

Abstract

We investigate a two parameter quantum deformation of the universal enveloping orthosymplectic superalgebra U(osp(2/2)) by extending the Faddeev-Reshetikhin-Takhtajan formalism to the supersymetric case. It is shown that $U_{p,q}(osp(2/2))$ possesses a non-commutative, non-cocommutative Hopf algebra structure. All the results are expressed in the standard form using quantum Chevalley basis.