2012/07/06 by Akira Masuoka, Masuoka, Akira
Mathematics · #16T05 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16T05
paper · pdf · doi:10.48550/arxiv.1207.1532
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
arxiv created 2012/07/06 · arxiv updated 2012/07/09
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.