Representations of finite dimensional pointed Hopf algebras over S3
Representations of finite dimensional pointed Hopf algebras over S3
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DOI：
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发表时间：
2010
影响因子：
0.5
通讯作者：
Agust'in Garc'ia Iglesias
中科院分区：
文献类型：
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作者：
Agust'in Garc'ia Iglesias
群为S3的有限维点Hopf代数的分类是在[AHS]中完成的：其中恰好有两种：12维Nichols代数的玻色化和非平凡提升。这里我们确定了任一Hopf代数上的所有单模。我们还找到了单模的射影覆盖--Gabriel箭图，并证明了它们不是有限表示型的。为此，我们首先研究了文献[AG1，GG]中定义的复点Hopf代数上的模，它们对类群群的限制是一维模的直和。
The classification of finite-dimensional pointed Hopf algebras with group S3 was finished in [AHS]: there are exactly two of them, the bosonization of a Nichols algebra of dimension 12 and a non-trivial lifting. Here we determine all simple modules over any of these Hopf algebras. We also find the Gabriel quivers, the projective covers of the simple modules, and prove that they are not of finite representation type. To this end, we first investigate the modules over some complex pointed Hopf algebras defined in the papers [AG1, GG], whose restriction to the group of group-likes is a direct sum of 1-dimensional modules.