Commuting varieties for nilpotent radicals

TL;DR

This paper extends the study of commuting varieties of Lie algebras associated with unipotent radicals from characteristic zero fields to fields with good characteristic, broadening the understanding of their algebraic structure.

Contribution

It generalizes previous results on commuting varieties for Lie(U) to fields with good characteristic, expanding the applicability of the theory.

Findings

Extended the properties of commuting varieties to positive characteristic fields

Demonstrated that the structure of commuting varieties remains consistent in good characteristic

Provided new insights into the algebraic geometry of unipotent radicals

Abstract

Let U be the unipotent radical of a Borel subgroup of a connected reductive algebraic group G, which is defined over an algebraically closed field k. In this paper, we extend work by Goodwin-R\"ohrle concerning the commuting variety of Lie(U) for char(k)=0 to fields, whose characteristic is good for G