A cohomological proof of Peterson-Kac's theorem of conjugacy of Cartan subalgebras of affine Kac-Moody Lie algebras

This paper deals with the problem of conjugacy of Cartan subalgebras for affine Kac-Moody Lie algebras. Unlike the methods used by Peterson and Kac, our approach is entirely cohomological and geometric. It is deeply rooted on the theory of reductive group schemes developed by Demazure and Grothendieck, and on the work of J. Tits on buildings.Fil: Chernousov, V.. University of Alberta; CanadáFil: Gille, P.. Centre National de la Recherche Scientifique. Ecole Normale Supérieure; FranciaFil: Pianzola, Arturo. University of Alberta; Canadá. Universidad Centro de Altos Estudios en Ciencias Exactas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Yahorau, U.. University of Alberta; Canad