Giovanna Carnovale, Universita' di
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.