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

Abstract

In this paper, we give an expansion of two notions of double extension and $T^{\ast }$-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.

18 pages, 1 table

References in corpus (3)

• Generalized double extension and descriptions of qadratic Lie superalgebras
• Jordanian double extensions of a quadratic vector space and symmetric Novikov algebras
• Singular quadratic Lie superalgebras