Cristian Vay

Finite Dimensional Hopf Algebras Over the Dual Group Algebra of the Symmetric Group in Three Letters

We classify finite-dimensional Hopf algebras whose coradical is isomorphic to the algebra of functions on 𝕊3. We describe a new infinite family of Hopf algebras of dimension 72.

The cohomology ring of the 12-dimensional Fomin–Kirillov algebra

Abstract The 12-dimensional Fomin–Kirillov algebra FK 3 is defined as the quadratic algebra with generators a , b and c which satisfy the relations a 2 = b 2 = c 2 = 0 and a b + b c + c a = 0 = b a + c b + a c . By a result of A. Milinski and H.-J. Schneider, this algebra is isomorphic to the Nichols algebra associated to the Yetter–Drinfeld module V , over the symmetric group S 3 , corresponding to the conjugacy class of all transpositions and the sign representation. Exploiting this identification, we compute the cohomology ring Ext FK 3 ⁎ ( k , k ) , showing that it is a polynomial ring S [ X ] with coefficients in the symmetric braided algebra of V . As an application we also compute the cohomology rings of the bosonization FK 3 # k S 3 and of its dual, which are 72-dimensional ordinary Hopf algebras.

From Hopf Algebras to Tensor Categories

This is a survey on spherical Hopf algebras. We give criteria to decide when a Hopf algebra is spherical and collect examples. We discuss tilting modules as a mean to obtain a fusion subcategory of the non-degenerate quotient of the category of representations of a suitable Hopf algebra.

ON PROJECTIVE MODULES OVER FINITE QUANTUM GROUPS

Let D

Copointed Hopf algebras over S4

\mathcal{D}

Hopf Algebras of Dimension 16

be the Drinfeld double of the bosonization 𝔙(V)𝕜G of a finite-dimensional Nichols algebra 𝔙(V ) over a finite group G. It is known that the simple D

On a family of Hopf algebras of dimension 72

\mathcal{D}