On pointed Hopf algebras over dihedral groups

FERNANDO FANTINO

Praga

Congreso; Quantum Theory and Symmetries (QTS-7); 2011

Czech Technical University in Prague and Academy of Sciences of the Czech Republic

Let k be an algebraically closed field of characteristic 0 and let Dm be the dihedral group of order 8t, with t>2. In this talk we will present the main results of a joint work with Gastón A. Gracía (F. Fantino and G. A. García, Pointed Hopf algebras over dihedral groups, Pacific J. Math., to appear): the classification of all finite-dimensional Nichols algebras over Dm and all finite-dimensional pointed Hopf algebras whose group of group-like elements isDm, by means of the Lifting method. As a byproduct we obtain new examples of finite-dimensional pointed Hopf algebras. In particular, we give an infinite family of non-abelian groups with non-trivial examples of pointed Hopf algebras over them and where the classification is completed.