Biproducts and Kashina's Examples

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.

Key Words:

• Biproduct
• Hopf algebra
• Smash product

2010 Mathematics Subject Classification:

• 16T05

Notes

Communicated by M. Cohen.