Factorisation properties of group scheme actions
Commutative Algebra
2011-02-01 v3
Abstract
Let H be an algebraic group scheme over a field k acting on a commutative k-algebra A which is a unique factorisation domain. We show that, under certain mild assumptions, the monoid of nonzero H-stable principal ideals in A is free commutative. From this we deduce, in certain special cases, results about the monoid of nonzero semi-invariants and the algebra of invariants.
Cite
@article{arxiv.1008.4292,
title = {Factorisation properties of group scheme actions},
author = {Rudolf Tange},
journal= {arXiv preprint arXiv:1008.4292},
year = {2011}
}