Giovanna Carnovale, Universita' di Padova

Title: Nichols algebras over finite simple groups

Abstract: Nichols algebras are a family of associative algebras defined by generators and relations depending on an endomorphism of a vector space V\otimes V satisfying the braid relation (braiding). They include exterior and symmetric algebras and  quantized Borel subalgebras. The algebras introduced by Fomin and Zelevinsky to study Schubert calculus for flag varieties for GL(n) are also strictly related to Nichols algebras.
For a group G a special class of braidings can  be associated with a G-module with a compatible G-grading. It has been conjectured that if G is finite simple non-abelian then all Nichols algebras obtained  this way are infinite-dimensional. I will describe the state of the art of this conjecture and present results obtained with  N. Andruskiewitsch and G. Garca and with Mauro Costantini for Suzuki and Ree for different families of finite simple groups.