Generalized double extension and descriptions of qadratic Lie superalgebras

TL;DR

This paper introduces a method to construct and describe quadratic Lie superalgebras using generalized double extensions, providing a new inductive approach to understanding their structure.

Contribution

It presents a novel inductive description of quadratic Lie superalgebras through generalized double extensions, expanding the theoretical framework.

Findings

Provides a systematic way to construct quadratic Lie superalgebras

Offers new insights into their structural properties

Enhances understanding of invariant bilinear forms in superalgebras

Abstract

A Lie superalgebra endowed with a supersymmetric, even, non-degenerate, invariant bilinear form is called a quadratic Lie superalgebra. In this paper we give inductive descriptions of quadratic Lie superalgebras in terms of generalized double extensions.