Non-noetherian GL-algebras in characteristic two

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.