Nichols algebras, pointed Hopf algebras and pointed tensor categories

IVÁN ANGIONO

Mar del Plata

Congreso; South American Meeting on Representations of Algebras and Related Topics; 2010

Univ. Nac. de Mar del Plata

We recall the notion of Nichols algebra, a graded algebra in the category of Yetter-Drinfeld modules over a Hopf algebra, and show its relation with semisimple Lie (super) algebras. We show also its importance for the classification of pointed Hopf algebras, and some properties about Nichols algebras of diagonal type, related with abelian groups. The category of comodules over a pointed Hopf algebra is an example of pointed tensor category. We review this kind of categories and show how the classification of pointed Hopf algebras is used to classify pointed tensor categories whose group of simple objects is cyclic.