Nichols algebras over simple groups

Abstract: Nichols (small shuffle) algebras are a family of graded algebras including the symmetric algebras, the exterior algebras, the positive part of quantized enveloping algebras. They are defined by generators and relations that depend on a vector space V and a solution of the braid equation on V\otimes V. A subclass of them, which is relevant for the classification program of finite-dimensional Hopf algebras developed by Andruskiewitsch and Schneider, consists of those for which the solution of the braid equation stems from a suitable graded representation of a finite group G. A folklore conjecture states that there are no non-trivial finite-dimensional Nichols algebras in this family if G is a non-abelian simple group. I will report on progress on this conjecture, based on a collaborations with N. Andruskiewitsch, G. García and M. Costantini.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar