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- W4210358629 abstract "Let G be a cyclic group of order p and let V,W be kG-modules. We study the modules of covariants k[V,W]G=(S(V⁎)⊗W)G. Recall that G has exactly p inequivalent indecomposable kG-modules, denoted Vn (n=1,…,p) and Vn has dimension n. For any n, we show that k[V2,Vn]G is a free k[V2]G-module (recovering a result of Broer and Chuai [1]) and we give an explicit set of covariants generating k[V2,Vn]G freely over k[V2]G. For any n, we show that k[V3,Vn]G is a Cohen-Macaulay k[V3]G-module (again recovering a result of Broer and Chuai) and we give an explicit set of covariants which generate k[V3,Vn]G freely over a homogeneous system of parameters for k[V3]G. We also use our results to compute a minimal generating set for the transfer ideal of k[V3]G over a homogeneous system of parameters." @default.
- W4210358629 created "2022-02-08" @default.
- W4210358629 creator A5002294253 @default.
- W4210358629 date "2022-05-01" @default.
- W4210358629 modified "2023-10-14" @default.
- W4210358629 title "Modular covariants of cyclic groups of order p" @default.
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- W4210358629 doi "https://doi.org/10.1016/j.jalgebra.2022.01.015" @default.
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