Mini-course on Hopf algebras--Hopf crossed products--
Mini-course on Hopf algebras--Hopf crossed products--
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Hopf代数迷你课程--Hopf交叉积--
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
A. Masuoka
中科院分区：
文献类型：
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作者：
A. Masuoka
Hopf交叉积，即裂模代数，在Hopf-伽罗瓦扩展中构成了一类特殊而重要的代数。为了讨论这个有趣的话题，我们将从更熟悉的群交叉积开始，然后看到它们自然地被霍普夫交叉积推广；这些Hopf交叉积被表征为具有正规基的Hopf- galois扩展。在展示了Doi和Takeuchi的这一特性之后，我们将继续讨论Hopf交叉积的两个应用——Hopf代数的等变光滑性，以及超交换Hopf超代数中的张量积分解。
Hopf crossed products, or in other words, cleft comodule algebras form a special but important class in Hopf-Galois extensions. To discuss this interesting subject, we will start with the more familiar group crossed products, and then see that they are naturally generalized by Hopf crossed products; these Hopf crossed products are characterized as Hopf-Galois extensions with normal basis. After showing this characterization due to Doi and Takeuchi, we will proceed to two applications of Hopf crossed products---the equivariant smoothness of Hopf algebras, and the tensor product decomposition in super-commutative Hopf superalgebras.