Epimorphic subgroups of algebraic groups

TL;DR

This paper characterizes epimorphic subgroups of algebraic groups via affinization, provides new criteria for affine algebraic groups, and extends the affinization theorem to homogeneous spaces.

Contribution

It establishes a precise description of epimorphic subgroups through affinization and generalizes existing results to broader contexts.

Findings

Epimorphic subgroups are pull-backs of those in affinization.

Provides new criteria for epimorphicity in affine algebraic groups.

Extends the affinization theorem to homogeneous spaces.

Abstract

In this note, we show that the epimorphic subgroups of an algebraic group are exactly the pull-backs of the epimorphic subgroups of its affinization. We also obtain epimorphicity criteria for subgroups of affine algebraic groups, which generalize a result of Bien and Borel. Moreover, we extend the affinization theorem for algebraic groups to homogeneous spaces.