Hopf algebra deformations of binary polyhedral groups

Details Hopf algebra deformations of binary polyhedral groups Hopf algebra deformations of binary polyhedral groups

2009-07-10

arxiv.org/abs/0907.1879v2

Mathematics

Quantum Algebra

revised version. Corrected proof of Proposition 3.2, a few changes in Subsection 4.2

Scientific paper

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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