Abstract view
Infinitesimal Invariants in a Function Algebra


Published:20090801
Printed: Aug 2009
Abstract
Let $G$ be a reductive connected linear algebraic group
over an algebraically closed field of positive
characteristic and let $\g$ be its Lie algebra.
First we extend a wellknown result about the Picard group of a
semisimple group to reductive groups.
Then we prove that if the derived group is simply connected
and $\g$ satisfies a
mild condition, the algebra $K[G]^\g$ of regular functions
on $G$ that are invariant under the action of $\g$ derived
from the conjugation action is a unique factorisation domain.