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arXiv · 1207.1532

Mini-course on Hopf algebras--Hopf crossed products--

Akira Masuoka
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Abstract

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.

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Akira Masuoka. 2012-07-06. Mini-course on Hopf algebras--Hopf crossed products--. https://arxiv.org/abs/1207.1532

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