Abstract
In this paper, we continue our study of the tensor product structure of category of weight modules over a Hopf–Ore extensions of a group algebra 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 χ and are different. Then we describe the Green ring of the tensor category . It is shown that is isomorphic to the polynomial algebra over the group ring in one variable when , and that is isomorphic to the quotient ring of the polynomial algebra over the group ring in two variables modulo a principle ideal when . When , is isomorphic to the quotient ring of a skew group ring modulo some ideal, where is a polynomial algebra over in infinitely many variables.
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