A presentation by generators and relations of Nichols algebras of diagonal type

IVÁN ANGIONO

Almería

Congreso; Conference on Hopf algebras and tensor categories; 2011

Universidad de Almería

The Lifting Method of Andruskiewitsch and Schneider is the leading method to classify pointed Hopf algebras [AS]. It involves as an inicial step to know for which braided vector spaces their associated Nichols algebra is nite-dimensional; such braided vector spaces were classied by Heckenberger [H]. A second step is the following one: for each of these Nichols algebras, give a nice presentation by generators a relations. In the present talk we give an answer to this question, following [A]. We characterize convex orders on root systems associated to nite Weyl groupoids and use a description of coideal subalgebras of Nichols algebras [HS]. We describe then a set of relations using the PBW bases of [Kh]. We use such presentation to prove that every nite-dimensional pointed Hopf algebra over C, whose group of group-like elements is abelian, is generated by its group-like and skew-primitive elements, a conjecture due to Andruskiewitsch and Schneider.