Separating polynomial invariants over non-closed fields of finite abelian groups
Commutative Algebra
2025-07-01 v1 Representation Theory
Abstract
It is proved that for any finite dimensional representation of a prime order group over the field of rational numbers, polynomial invariants of degree at most separate the orbits. A result providing an upper degree bound for separating invariants for representations of finite abelian groups over algebraically closed base fields of non-modular characteristic is generalized for the case of base fields that are not algebraically closed (like the fields of real or rational numbers).
Keywords
Cite
@article{arxiv.2506.22889,
title = {Separating polynomial invariants over non-closed fields of finite abelian groups},
author = {Mátyás Domokos},
journal= {arXiv preprint arXiv:2506.22889},
year = {2025}
}