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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 (v1⊕v2)g=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...
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