The Cell Modules of the Green Algebra of Drinfel'd Quantum Double D(H_4)
The Cell Modules of the Green Algebra of Drinfel'd Quantum Double D(H_4)
复制标题
Drinfel'd量子双D(H_4)的绿色代数的元胞模
DOI：
10.1007/s10114-022-9046-8
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Li Libin
中科院分区：
文献类型：
--
作者：
Cao Liufeng;Chen Huixiang;Li Libin
本文研究复化Green代数R(D(H_4))的胞模的结构，其中D(H_4)是Sweedler‘s四维Hopf代数H_4的Drinfel’d量子偶.我们证明了R(D(H_4))有一个无限维胞模，一个由D(H_4)的所有有限维不可分解投射模生成的四维胞模和无穷多个二维胞模.更确切地说，我们得到了所有有限维胞体模分解为不可分解子模的直和，并证明了无限维胞体模可以表示为两个无限维不可分解子模的直和。
This paper is devoted to studying the structures of the cell modules of the complexified Green algebra R(D(H_4)), where D(H_4) is the Drinfel'd quantum double of Sweedler’s 4-dimensional Hopf algebra H_4. We show that R(D(H_4)) has one infinite dimensional cell module, one 4-dimensional cell module generated by all finite dimensional indecomposable projective modules of D(H_4) and infinitely many 2-dimensional cell modules. More precisely, we obtain the decompositions of all finite dimensional cell modules into the direct sum of indecomposable submodules, and show that the infinite dimensional cell module can be written as the direct sum of two infinite dimensional indecomposable submodules.