Restricted simple Lie (super)algebras in characteristic $3$

TL;DR

This paper provides explicit formulas demonstrating the restrictedness of various exceptional simple Lie (super)algebras and their subquotients in characteristic 3, expanding understanding of their structure and properties.

Contribution

It introduces explicit formulas proving restrictedness for known exceptional simple vectorial Lie (super)algebras and their subquotients in characteristic 3, including deformed and divergence-free types.

Findings

Explicit formulas for restrictedness in characteristic 3

Extension to deformed Lie (super)algebras with Cartan matrix

Analysis of divergence-free Lie superalgebras with multiple indeterminates

Abstract

We give explicit formulas proving restrictedness of the following Lie (super)algebras: known exceptional simple vectorial Lie (super)algebras in characteristic 3, deformed Lie (super)algebras with indecomposable Cartan matrix, and (under certain conditions) their simple subquotients over an algebraically closed field of characteristic 3, as well as one type of the deformed divergence-free Lie superalgebras with any number of indeterminates in any characteristic.