Singular quadratic Lie superalgebras

TL;DR

This paper generalizes previous results on quadratic Lie superalgebras by introducing a numerical invariant, classifying singular cases, and exploring their construction via generalized double extensions.

Contribution

It extends the theory of quadratic Lie superalgebras using graded Lie algebra tools, providing a classification of singular cases and new construction methods.

Findings

Introduces a numerical invariant for quadratic Lie superalgebras

Classifies singular quadratic Lie superalgebras with nonzero invariant

Studies quadratic Lie superalgebras via generalized double extensions

Abstract

In this paper, we give a generalization of results in \cite{PU07} and \cite{DPU10} by applying the tools of graded Lie algebras to quadratic Lie superalgebras. In this way, we obtain a numerical invariant of quadratic Lie superalgebras and a classification of singular quadratic Lie superalgebras, i.e. those with a nonzero invariant. Finally, we study a class of quadratic Lie superalgebras obtained by the method of generalized double extensions.