Anti-affine algebraic groups

Abstract

We say that an algebraic group $G$ over a field is anti-affine if every regular function on $G$ is constant. We obtain a classification of these groups, with applications to the structure of algebraic groups in positive characteristics, and to the construction of many counterexamples to Hilbert's fourteenth problem.

Prior work of Carlos Sancho de Salas acknowledged, additional minor changes,

Cited by in corpus (2)

• Observable actions of algebraic groups
• The ring of regular functions of an algebraic monoid