Manin supertriples and Drinfel'd superdoubles in low dimensions

TL;DR

This paper classifies low-dimensional real Manin supertriples and Drinfel'd superdoubles, providing foundational structures for constructing sigma-models on supergroups connected through Poisson-Lie T-plurality.

Contribution

It offers a complete classification of real Manin supertriples and Drinfel'd superdoubles in specific low dimensions, advancing the understanding of their structure.

Findings

Classified supertriples and superdoubles in dimensions (2,2), (4,2), and (2,4)

Established their use in constructing sigma-models on supergroups

Linked structures via Poisson-Lie T-plurality

Abstract

Defining the real Lie superalgebra as real $Z_2$--graded vector space we classify real Manin supertriples and Drinfel'd superdoubles of superdimensions (2,2), (4,2) and (2,4). They can be used for construction of sigma-models on supergroups related by Poisson-Lie T-plurality.