Orateur
M.
Philippe ROCHE
(IMAG)
Description
We prove that the graph algebra and the quantum moduli
algebra associated to a punctured sphere and complex semisimple Lie
algebra $\mathfrak{g}$ are Noetherian rings and finitely generated
rings over $\mc(q)$. Moreover, we show that these two properties still
hold on $\mc[q,q^{-1}]$ for the integral version of the graph algebra.
We also study the specializations $\Ll_{0,n}^\e$ of the graph algebra
at a root of unity $\e$ of odd order, and show that $\Ll_{0,n}^\e$ and
its invariant algebra under the quantum group $U_\e(\mathfrak{g})$
have classical fraction algebras which are central simple algebras of
PI degree that we compute.
