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

Vladimir Chernousov (1) , Vladimir Egorov (1) , Philippe Gille (2) , Arturo Pianzola (1)

1 University of Alberta
2 DMA - Département de Mathématiques et Applications - ENS Paris

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.

Mots clés: Affine Kac-Moody algebras; Conjugacy; Reductive Group Schemes; Torsor; Laurent Polynomials; Non-abelian Cohomology

Domaines: Anneaux et algèbres [math.RA]

Vladimir Chernousov, Vladimir Egorov, Philippe Gille, Arturo Pianzola. A cohomological proof of Peterson-Kac's theorem on conjugacy of Cartan subalgebras of affine Kac-Moody Lie algebras. 2012. ⟨hal-00693938⟩