On Hopf algebras of dimension 4p
On Hopf algebras of dimension 4p
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DOI：
10.1016/j.jalgebra.2010.08.029
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发表时间：
2010-05
影响因子：
0.9
通讯作者：
Yi-Lin Cheng;S. Ng
中科院分区：
文献类型：
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作者：
Yi-Lin Cheng;S. Ng
本文证明了特征为零的代数闭域上的4p维非半单Hopf代数H（p为奇素数）是有指向性的，只要H包含两个以上的类群元.特别地，我们证明了20，28和44维的非半单Hopf代数是尖的或它们的顶点是尖的，这完成了这些维的Hopf代数的分类。
In this paper, we prove that a non-semisimple Hopf algebra H of dimension 4p with p an odd prime over an algebraically closed field of characteristic zero is pointed provided H contains more than two group-like elements. In particular, we prove that non-semisimple Hopf algebras of dimensions 20, 28 and 44 are pointed or their duals are pointed, and this completes the classification of Hopf algebras in these dimensions.