## On a family of Hopf algebras of dimension 72.(English)Zbl 1282.16036

The authors apply the lifting method to investigate a family of Hopf algebras of dimension $$72$$ whose coradical is isomorphic to the algebra of functions on $$\mathbb S_3$$. It is determined the lattice of submodules of the so-called Verma modules. As a consequence the authors classify all simple modules. It is shown that these Hopf algebras are unimodular (as well as their duals) but not quasitriangular; also, they are cocycle deformations of each other.
It is believed that the representation theory of Hopf algebras with coradical which is isomorphic to the algebra of functions on a group $$G$$ might be helpful to study Nichols algebras and deformations.

### MSC:

 16T05 Hopf algebras and their applications
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