Varieties of elementary subalgebras of maximal dimension for modular Lie algebras

TL;DR

This paper characterizes the varieties of maximal dimension abelian p-nilpotent subalgebras in reductive restricted Lie algebras, advancing understanding in modular representation theory.

Contribution

It identifies the varieties E(r, g) for reductive restricted Lie algebras when r is the maximal dimension of such subalgebras, providing a classification.

Findings

Explicit description of E(r, g) for reductive g

Connection to modular representation theory

Advancement in understanding elementary subalgebras

Abstract

Motivated by questions in modular representation theory, Carlson, Friedlander, and the first author introduced the varieties E(r, g) of r-dimensional abelian p-nilpotent subalgebras of a p-restricted Lie algebra g. In this paper, we identify the varieties E(r, g) for a reductive restricted Lie algebra g and r the maximal dimension of an abelian p-nilpotent subalgebra of g.