Université de l’Alberta, 24 - 27 juin 2016
This was generalized by Allison, Berman, Faulkner and Pianzola to arbitrary nonassociative algebras and arbitrary quotients of abelian groups. In view of their results, the recent classification of gradings by arbitrary abelian groups on finite-dimensional simple Lie algebras (over an algebraically closed field of charactersitic zero) yields a classification of finite-dimensional graded-simple Lie algebras.
Mazorchuk and Zhao have recently applied the loop construction to modules. In this talk, we will show how this leads to a classification of finite-dimensional graded-simple modules over simple Lie algebras with a grading. This is joint work with Alberto Elduque.
We show that the category of the Temperley-Lieb algebras is braided and that this braiding can be extended naturally to a category of modules over the family for the product introduced by Read and Saleur.
Joint work with J. Bellet\^ete.
Based on work done in collaboration with H. De Bie (Ghent), V. X. Genest (MIT), J.-M. Lemay (CRM).