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

[摘要] Let V = V(1) circle plus V(2) be a finite-dimensional vector space over an infinite locally-finite field F. Then V admits the torus action of G = F(center dot) by defining (v(1) circle plus v(2))(g) = v(1)g(-1) circle plus v(2)g. If K is a field of characteristic different from that of F, then G acts on the group algebra Kinverted right perpendicularVinverted left perpendicular and it is an interesting problem to determine all G-stable ideals of this algebra. In this paper, we consider the special case when V(1) and V(2) are both 1-dimensional and we show that there are just four G-stable proper ideals of Kinverted right perpendicularVinverted left perpendicular. (C) 2010 Elsevier Inc. All rights reserved.

[发布日期] 2010-12-01

[关键词] Group algebra;Group action;Torus action;Invariant ideal