New twisted quantum deformations of D=4 super-Poincare algebra

TL;DR

This paper introduces new quantum deformations of the D=4 super-Poincare algebra by supersymmetrizing classical r-matrices, resulting in explicit super-extensions of known twists with potential applications in quantum symmetry studies.

Contribution

It presents novel supersymmetric r-matrices for the D=4 super-Poincare algebra and constructs explicit twists for their quantum deformations, extending previous work.

Findings

Supersymmetrized classical r-matrices for D=4 super-Poincare algebra.

Explicit forms of the corresponding quantum twists.

Extension of previous twist constructions to superalgebra context.

Abstract

We show how some classical r-matrices for the D=4 Poincare algebra can be supersymmetrized by an addition of part depending on odd supercharges. These r-matrices for D=4 super-Poincare algebra can be presented as a sum of the so-called subordinated r-matrices of super-Abelian and super-Jordanian type. Corresponding twists describing quantum deformations are obtained in an explicit form. These twists are the super-extensions of twists obtained in the paper arXiv:0712.3962.