Closure of Certain Matrix Varieties and Applications

TL;DR

This paper studies the closures of matrix varieties with fixed centralizer dimensions, generalizing previous results, and explores their applications in the topological generation of simple algebraic groups.

Contribution

It extends known results on matrix varieties and applies these findings to the theory of simple algebraic groups.

Findings

Generalizes Dixmier's result on matrix varieties

Provides new insights into the structure of matrix varieties with fixed centralizer dimensions

Applications to the topological generation of simple algebraic groups

Abstract

We prove some results about closures of certain matrix varieties consisting of elements with the same centralizer dimension. This generalizes a result of Dixmier and has applications to topological generation of simple algebraic groups.