Hopf Algebra Deformations of Binary Polyhedral Groups
نویسندگان
چکیده
We show that semisimple Hopf algebras having a self-dual faithful irreducible comodule of dimension 2 are always obtained as abelian extensions with quotient Z2. 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.
منابع مشابه
Quantum deformations of the Lorentz group . The Hopf ∗ - algebra level
Three properties characteristic for the Lorentz group are selected and all quantum groups with the same properties are found. As a result, a number of one, two and three parameter quantum deformations of the Lorentz group are discovered. The deformations described in [1] and [2] are among them. Only the Hopf ∗-algebra level is discussed.
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