Inhomogeneous supersymmetric bilinear forms

TL;DR

This paper classifies inhomogeneous supersymmetric bilinear forms up to dimension seven and introduces a new oscillator Lie superalgebra based on these forms.

Contribution

It provides a classification of inhomogeneous supersymmetric bilinear forms and introduces a novel oscillator Lie superalgebra.

Findings

Classification of forms up to dimension seven

Introduction of a new oscillator Lie superalgebra

Forms are nondegenerate on even and odd parts

Abstract

We consider inhomogeneous supersymmetric bilinear forms, i.e., forms that are neither even nor odd. We classify such forms up to dimension seven in the case when the restrictions of the form to the even and odd parts of the superspace are nondegenerate. As an application, we introduce a new type of oscillator Lie superalgebra.