Models of some simple modular Lie superalgebras

TL;DR

This paper constructs models for certain exceptional simple modular Lie superalgebras in characteristic p≥3, linking them to low-dimensional nonassociative algebraic systems and aiding their classification.

Contribution

It provides explicit models for exceptional simple modular Lie superalgebras, connecting them to nonassociative algebraic systems and expanding understanding of their structure.

Findings

Models relate exceptional Lie superalgebras to low-dimensional nonassociative systems

Clarifies structure of Lie superalgebras with indecomposable symmetrizable Cartan matrices

Supports classification of modular Lie superalgebras in characteristic p≥3

Abstract

Models of the exceptional simple modular Lie superalgebras in characteristic $p\geq 3$, that have appeared in the classification due to Bouarroudj, Grozman and Leites of the Lie superalgebras with indecomposable symmetrizable Cartan matrices, are provided. The models relate these exceptional Lie superalgebras to some low dimensional nonassociative algebraic systems.