Multiparameter Quantum Deformations of Jordanian Type for Lie Superalgebras

TL;DR

This paper explores multiparameter quantum deformations of Jordanian type for Lie superalgebras, providing explicit twist constructions and identifying Jordanian structures in super-Poincare algebra deformations.

Contribution

It introduces explicit multiparameter Jordanian twists for Lie superalgebras and applies these to the super-Poincare algebra's light-cone deformation.

Findings

Explicit forms of total twists for sl(m|n) and osp(1|2n)

Identification of Jordanian type r-matrix in super-Poincare algebra

Demonstration of multiparameter deformation structures

Abstract

We discuss quantum deformations of Jordanian type for Lie superalgebras. These deformations are described by twisting functions with support from Borel subalgebras and they are multiparameter in the general case. The total twists are presented in explicit form for the Lie superalgebras sl(m|n) and osp(1|2n). We show also that the classical $r$-matrix for a light-cone deformation of D=4 super-Poincare algebra is of Jordanian type and a corresponding twist is given in explicit form.