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تسجيل مستخدم جديدTensor product decomposition rules for weight modules over the Hopf-Ore extensions of group algebras
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In this paper, we investigate the tensor structure of the category of finite dimensional weight modules over the Hopf-Ore extensions $kG(chi^{-1}, a, 0)$ of group algebras $kG$. The tensor product decomposition rules for all indecomposable weight modules are explicitly given under the assumptions that $k$ is an algebraically closed field of characteristic zero, and the orders of $chi$ and $chi(a)$ are the same.
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In this paper, we continue our study of the tensor product structure of category $mathcal W$ of weight modules over the Hopf-Ore extensions $kG(chi^{-1}, a, 0)$ of group algebras $kG$, where $k$ is an algebraically closed field of characteristic zero
. We first describe the tensor product decomposition rules for all indecomposable weight modules under the assumption that the orders of $chi$ and $chi(a)$ are different. Then we describe the Green ring $r(mathcal W)$ of the tensor category $mathcal W$. It is shown that $r(mathcal W)$ is isomorphic to the polynomial algebra over the group ring $mathbb{Z}hat{G}$ in one variable when $|chi(a)|=|chi|=infty$, and that $r(mathcal W)$ is isomorphic to the quotient ring of the polynomial algebra over the group ring $mathbb{Z}hat{G}$ in two variables modulo a principle ideal when $|chi(a)|<|chi|=infty$. When $|chi(a)|le|chi|<infty$, $r(mathcal W)$ is isomorphic to the quotient ring of a skew group ring $mathbb{Z}[X]sharphat{G}$ modulo some ideal, where $mathbb{Z}[X]$ is a polynomial algebra over $mathbb{Z}$ in infinitely many variables.
In this paper, we study the representations of the Hopf-Ore extensions $kG(chi^{-1}, a, 0)$ of group algebra $kG$, where $k$ is an algebraically closed field. We classify all finite dimensional simple $kG(chi^{-1}, a, 0)$-modules under the assumption
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