Green ring of the category of weight modules over the Hopf–Ore extensions of group algebras
Green ring of the category of weight modules over the Hopf–Ore extensions of group algebras
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DOI：
10.1080/00927872.2018.1534121
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发表时间：
2018-06
影响因子：
0.7
通讯作者：
Hua Sun;Hui-xiang Chen
中科院分区：
文献类型：
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作者：
Hua Sun;Hui-xiang Chen
本文继续研究了群代数kG的Hopf-Ore扩展上权模范畴的张量积结构，其中k是特征为零的代数闭域。我们首先在x和的阶数不同的假设下，描述了所有不可分解权重模块的张量积分解规则。然后描述张量范畴的绿环。证明了在单变量群环上的多项式代数同构，在双变量群环上的多项式代数的商环同构。时，同构于模于某理想的斜群环的商环，其中为无穷多变量上的多项式代数。
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.