A classification of quadratic and odd quadratic Lie superalgebras in low dimensions

TL;DR

This paper extends the concepts of double and T*-extensions to quadratic and odd quadratic Lie superalgebras and classifies such superalgebras up to dimension 6, focusing on solvable, indecomposable cases.

Contribution

It introduces expanded notions of double and T*-extensions for quadratic and odd quadratic Lie superalgebras and provides a detailed classification up to dimension 6.

Findings

Classification of quadratic and odd quadratic Lie superalgebras up to dimension 6

Extension of double and T*-extensions to superalgebras

Identification of indecomposable, solvable superalgebras

Abstract

In this paper, we give an expansion of two notions of double extension and $T^*$-extension for quadratic and odd quadratic Lie superalgebras. Also, we provide a classification of quadratic and odd quadratic Lie superalgebras up to dimension 6. This classification is considered up to isometric isomorphism, mainly in the solvable case and the obtained Lie superalgebras are indecomposable.