2014/02/19 by David E. Radford, Radford, David E. · 1 citation
Mathematics · Physics and Astronomy · #16T05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1402.4714
openalex publication_date 2014/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We revisit a class of examples described in the original paper 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 of dimension a power of two determined by Kashina are examined. The finite-dimensional non-trivial 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.