Non-noetherian GL-algebras in characteristic two

TL;DR

This paper constructs the first known example of a non-noetherian GL-algebra over fields of characteristic two by creating an infinite chain of GL-stable ideals in the coordinate ring of infinite skew-symmetric matrices, resolving a long-standing open question.

Contribution

It provides the first explicit example of a non-noetherian GL-algebra in characteristic two, advancing understanding of algebraic structures under group actions.

Findings

Established the existence of a non-noetherian GL-algebra in characteristic two.

Constructed an infinite ascending chain of GL-stable ideals.

Resolved a long-standing open problem in the field.

Abstract

Over fields of characteristic two, we construct an infinite ascending chain of GL-stable ideals in the coordinate ring of infinite skew-symmetric matrices. This construction provides the first known example of a non-noetherian GL-algebra, thereby resolving a long-standing open question in the area. Our results build on the work of Draisma, Krasilnikov, and Krone.