Biproducts and Kashina's Examples. Issue 1 (2nd January 2016)

• Record Type: Journal Article
• Authors: Radford, David E.
• Is Part Of: Communications in algebra. Volume 44:Issue 1(2016)
• Page Start: 174
• Page End: 204
• Publication Date: 2016-01-02
• Subjects: Biproduct -- Hopf algebra -- Smash product; 16T05; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2014.974252
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract : We revisit a class of examples described in the original article on biproducts, expand the class, and provide a detailed analysis of the coalgebra and algebra structures of many of these examples. Connections with the semisimple Hopf algebras whose dimension is a power of two determined by Kashina are examined. The finite-dimensional nontrivial semisimple cosemisimple Hopf algebras we construct are shown to be lower cosolvable. Some of these have one proper normal Hopf subalgebra and are not lower solvable.