Invariant ideals of abelian group algebras under the torus action of a field, II

Let V=V1⊕V2 be a finite-dimensional vector space over an infinite locally-finite field F. Then V admits the torus action of G=F• by defining g(v1⊕v2)=v1g−1⊕v2g. If K is a field of characteristic different from that of F, then G acts on the group algebra K[V] and it is an interesting problem to determine all G-stable ideals of this algebra. In this paper, we show that, for almost all fields F, the G-stable ideals are uniquely writable as finite irredundant intersections of augmentation ideals of subspaces W1⊕W2, with W1⊆V1 and W2⊆V2. As a consequence, the set of all G-stable ideals is Noetherian.