Self-Dual Hopf Algebras of Dimension p3 Obtained by Extension
Self-Dual Hopf Algebras of Dimension p3 Obtained by Extension
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DOI：
10.1006/jabr.1995.1378
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发表时间：
1995-12
影响因子：
0.9
通讯作者：
A. Masuoka
中科院分区：
文献类型：
--
作者：
A. Masuoka
我们在代数闭域k上工作。最近，半单Hopf代数（k上）[LR 2，ZS，ZY，M2，M3]的分类取得了一些进展。例如，朱[ZY]和作者[M3]证明了，当特征chk为0时，一个维数为p或p”且素数为p的半单Hopf代数是交换的和余交换的，因此它是由交换类群张成的。文[M2]还证明了在chk = 2的假设下，只存在一个既不是交换的也不是余交换的8维半单Hopf代数.
We work over an algebraically closed field k. Recently there is some progress in classification of semisimple Hopf algebras (over k)[LR2, ZS, ZY, M2, M3]. For example it is shown by Zhu [ZY] and the author [M3] that in the case where the characteristic ch k is 0 a semisimple Hopf algebra of dimension p or p" with a prime p is commutative and cocommutative, and so it is spanned by commutative group-likes. It is also shown by the author [M2] under the assumption ch k= 2 that there exists only one semisimple Hopf algebra of dimension 8 which is neither commu-tative nor cocommutative.