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Simple Hopf algebras and deformations of finite groups

Cesar N. Galindo·Sonia Natale
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Abstract

We show that certain twisting deformations of a family of supersolvable groups are simple as Hopf algebras. These groups are direct products of two generalized dihedral groups. Examples of this construction arise in dimensions 60 and p^2q^2, for prime numbers p, q with q dividing p-1. We also show that certain twisting deformation of the symmetric group is simple as a Hopf algebra. On the other hand, we prove that every twisting deformation of a nilpotent group is semisolvable. We conclude that the notions of simplicity and (semi)solvability of a semisimple Hopf algebra are not determined by its tensor category of representations.

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Cesar N. Galindo, Sonia Natale. 2006-09-07. Simple Hopf algebras and deformations of finite groups. https://arxiv.org/abs/math/0608734

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