The Tits construction and some simple Lie superalgebras in characteristic 3

TL;DR

This paper explores the relationship between certain simple Lie superalgebras in characteristic 3 and simple alternative and commutative superalgebras, revealing new structural connections in algebra.

Contribution

It establishes a link between characteristic 3 Lie superalgebras and superalgebras discovered by Shestakov, expanding understanding of algebraic structures in this characteristic.

Findings

Connection between characteristic 3 Lie superalgebras and Shestakov's superalgebras

Identification of structural similarities in algebraic properties

Enhanced classification of simple superalgebras in characteristic 3

Abstract

Some simple Lie superalgebras, specific of characteristic 3, defined by S. Bouarroudj and D. Leites, are shown to be related to the simple alternative and commutative superalgebras discovered by I.P. Shestakov.