Giovanna Carnovale (Universidad de Padova, Italia)

Jueves 4 de julio 14.30hs. Aula 27.

joint work with Mauro Costantini, part of a long-term project with Nicolás Andruskiewitsch and Gastón Garcia.

Andruskiewitsch and Graña have shown that Nichols algebras can be constructed starting from a rack X and a 2-cocycle on X. Several conditions (type C, D or F) on a rack X have been proved to ensure that the associated Nichols algebras are infinite-dimensional for any choice of the cocycle. Since this criteria are well-behaved with respect to projections and inclusions, it is of great interest to understand which simple racks satisfy one of these conditions. Among simple racks we have the family of conjugacy classes in a non-ablelian finite simple group with rack structure x>y=xyx^{-1}. In this case  these conditions are easily stated in group theoretic terms. Suzuki and Ree  groups form three families of simple groups of Lie type, associated with root systems of type B2, F4 and G2 and a Coxeter graph automorphism. After recalling the state of the art concerning the other families of finite simple groups, we will discuss the problem of listing which classes are of type C, D, or F in  Suzuki and Ree groups and the related question of the existence of finite-dimensional pointed Hopf algebras whose group of grouplikes is one of them.