Finite generalized root systems and applications

This talk is based in a work in progress with Nicolás Andruskiewitsch. 

We review the definition of generalized root system (GRS for short), due to Heckenberger and Yamane. Then we show that contragredient Lie superalgebras (over fields of arbitrary characterisric) and Nichols algebras of diagonal type give rise to GRS. We discuss how to use this fact for the classification of both kinds of algebras (in the finite-dimensional context).