Classification of two and three dimensional Lie super-bialgebras

TL;DR

This paper classifies all two and three dimensional Lie super-bialgebras by deriving their identities through adjoint representations and automorphism supergroups, providing a comprehensive structural understanding.

Contribution

It introduces a systematic method for classifying low-dimensional Lie super-bialgebras using matrix forms and automorphism supergroups, filling a gap in the literature.

Findings

Complete classification of 2D and 3D Lie super-bialgebras.

Derived matrix forms of super-Jacobi identities.

Identified automorphism supergroups for these algebras.

Abstract

Using adjoint representation of Lie superalgebras, we obtain the matrix form of super-Jacobi and mixed super-Jacobi identities of Lie superbialgebras. By direct calculations of these identities, and use of automorphism supergroups of two and three dimensional Lie superalgebras, we obtain and classify all two and three dimensional Lie superbialgebras.