Initial forms of stable invariants for additive group actions

TL;DR

This paper extends the Derksen--Hadas--Makar-Limanov theorem, showing that stable invariants under additive group actions also lack intruders, thus broadening understanding of polynomial invariants.

Contribution

It generalizes the classical theorem to stable invariants, providing new insights into additive group actions on polynomial rings.

Findings

Stable invariants have no intruder

Generalization of the Derksen--Hadas--Makar-Limanov theorem

Enhanced understanding of polynomial invariants under additive group actions

Abstract

The Derksen--Hadas--Makar-Limanov theorem (2001) says that the invariants for nontrivial actions of the additive group on a polynomial ring have no intruder. In this paper, we generalize this theorem to the case of stable invariants.