Classification of four and six dimensional Drinfel'd superdoubles

TL;DR

This paper completes the classification of four and six dimensional Drinfel'd superdoubles by using adjoint representation to classify related Lie super-bialgebras, extending previous work on lower dimensions.

Contribution

It introduces a comprehensive classification of four and six dimensional Drinfel'd superdoubles, building upon prior classifications of lower-dimensional Lie super-bialgebras.

Findings

Complete classification of four and six dimensional Drinfel'd superdoubles.

Extension of previous classifications to higher dimensions.

Utilization of adjoint representation for classification.

Abstract

Using adjoint representation we firstly classify two and three dimensional Lie super-bialgebras obtain from decomposable Lie superalgebras. In this way we complete the classification obtained by Eghbali et al., [J. Math. Phys. 51, 073503 (2010); e-print arXiv:0901.4471 [math-ph]]. Then we classify all four and six dimensional Drinfel'd superdoubles.