Separating algebras and finite reflection groups
Commutative Algebra
2016-02-01 v3 Algebraic Geometry
Abstract
A separating algebra is, roughly speaking, a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this paper, we introduce a geometric notion of separating algebra. This allows us to prove that only groups generated by reflections may have polynomial separating algebras, and only groups generated by bireflections may have complete intersection separating algebras.
Cite
@article{arxiv.0805.2605,
title = {Separating algebras and finite reflection groups},
author = {Emilie Dufresne},
journal= {arXiv preprint arXiv:0805.2605},
year = {2016}
}
Comments
12 pages, corrected yet another typo