# Maximally extended sl(2|2), q-deformed d(2,1;epsilon) and 3D kappa-Poincar\'e

## TL;DR

This paper constructs a maximal extension of the superalgebra sl(2|2) via contraction limits from d(2,1;epsilon) and explores its relation to kappa-Poincaré symmetry, including a new deformation and explicit R-matrix.

## Contribution

It introduces a novel maximal extension of sl(2|2) through contraction from d(2,1;epsilon), revealing new connections to kappa-Poincaré algebra and providing explicit formulas for the universal R-matrix.

## Key findings

- Maximal extension of sl(2|2) obtained as contraction limit.
- New one-parameter deformation of 3D kappa-Poincaré algebra.
- Explicit expression for the universal R-matrix.

## Abstract

We show that the maximal extension sl(2) times psl(2|2) times C3 of the sl(2|2) superalgebra can be obtained as a contraction limit of the semi-simple superalgebra d(2,1;epsilon) times sl(2). We reproduce earlier results on the corresponding q-deformed Hopf algebra and its universal R-matrix by means of contraction. We make the curious observation that the above algebra is related to kappa-Poincar\'e symmetry. When dropping the graded part psl(2|2) we find a novel one-parameter deformation of the 3D kappa-Poincar\'e algebra. Our construction also provides a concise exact expression for its universal R-matrix.