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.
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Communicated by M. Cohen.