The five exceptional simple Lie superalgebras of vector fields

TL;DR

This paper classifies five exceptional simple Lie superalgebras of vector fields, describing four for the first time and introducing one new algebra, using Cartan prolongation methods.

Contribution

It provides explicit descriptions of four previously uncharacterized exceptional Lie superalgebras and introduces a new one, expanding the understanding of these algebraic structures.

Findings

Four exceptional Lie superalgebras described for the first time

One new exceptional Lie superalgebra identified

All are constructed via Cartan or generalized prolongation

Abstract

The five simple exceptional complex Lie superalgbras of vector fields are described. One of them is new; the other four are explicitely described for the first time. All of the exceptional Lie superalgebras are obtained with the help of the Cartan prolongation or a generalized prolongation. The description of several of the exceptional Lie superalgebras is associated with the Lie superalgebra AS - the nontrivial central extension of the supertraceless subalgebra SPE(4) of the periplectic Lie superalgebra PE(4) that preserves the nondegenerate odd bilinear form on the (4|4)-dimensional superspace. (A nontrivial central extension of SPE(n) only exists for n=4.)