Sonia Natale

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These notes contain the material presented in a series of five lectures at the University of Córdoba in September 1994. The intent of this brief course was to give a quick introduction to Hopf algebras and to prove as directly as possible (to me) some recent results on finitedimensional Hopf algebras conjectured by Kaplansky in 1975. In particular, in the(More)
We survey some aspects of the theory of Hopf-Galois objects that may studied advantageously by using the language of cogroupoids. These are the notes for a series of lectures given at Cordobá University, may 2010. The lectures are part of the course “HopfGalois theory” by Sonia Natale.
We show that certain twisting deformations of a family of supersolvable groups are simple as Hopf algebras. These groups are direct products of two generalized dihedral groups. Examples of this construction arise in dimensions 60 and pq, for prime numbers p, q with q|p − 1. We also show that certain twisting deformation of the symmetric group is simple as a(More)
The construction of a quantum groupoid out of a double groupoid satisfying a filling condition and a perturbation datum is given. Several important classes of examples of tensor categories are shown to fit into this construction. Certain invariants such as a pivotal grouplike element and quantum and Frobenius-Perron dimensions of simple objects are computed.