Hopf algebra deformations of binary polyhedral groups

JULIEN BICHON Y SONIA NATALE

TRANSFORMATION GROUPS

BIRKHAUSER BOSTON INC

Año: 2011 vol. 16 p. 339 - 374

1083-4362

We show that semisimple Hopf algebras having a self-dual faithful irreduciblecomodule of dimension 2 are always obtained as abelian extensions with quotient Z2. Weprove that nontrivial Hopf algebras arising in this way can be regarded as deformationsof binary polyhedral groups and describe its category of representations. We also prove astrengthening of a result of Nichols and Richmond on cosemisimple Hopf algebras with atwo-dimensional irreducible comodule in the nite-dimensional context. Finally, we givesome applications to the classication of certain classes of semisimple Hopf algebras.