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arXiv · 0907.1879

Hopf algebra deformations of binary polyhedral groups

Julien Bichon·Sonia Natale
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Abstract

We show that semisimple Hopf algebras having a self-dual faithful irreducible comodule of dimension 2 are always obtained as abelian extensions with quotient Z_2. We prove that nontrivial Hopf algebras arising in this way can be regarded as deformations of binary polyhedral groups and describe its category of representations. We also prove a strengthening of a result of Nichols and Richmond on cosemisimple Hopf algebras with a 2-dimensional irreducible comodule in the finite dimensional context. Finally, we give some applications to the classification of certain classes of semisimple Hopf algebras.

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Julien Bichon, Sonia Natale. 2010-11-23. Hopf algebra deformations of binary polyhedral groups. https://arxiv.org/abs/0907.1879

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