Invariant Ideals of Abelian Group Algebras under the Torus Action of a Field, I
نویسنده
چکیده
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) = 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 consider the special case when V1 and V2 are both 1-dimensional and we show that there are just four G-stable proper ideals of K[V ].
منابع مشابه
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 (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 ...
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