English

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

Rings and Algebras 2012-07-09 v1

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.

Keywords

Cite

@article{arxiv.1207.1532,
  title  = {Mini-course on Hopf algebras--Hopf crossed products--},
  author = {Akira Masuoka},
  journal= {arXiv preprint arXiv:1207.1532},
  year   = {2012}
}

Comments

The notes based on the author's talks at the Conference on Ring Theory held at the Sun Yat-Sen University, Guangzhou in P. R. China, June 24--30, 2012