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

JOURNAL OF ALGEBRA

卷:399

Article

Chernousov, V.¹  Gille, P.²  Pianzola, A.^1,3  Yahorau, U.¹ 

[1] Univ Alberta, Dept Math, Edmonton, AB T6G 2G1, Canada

[2] Ecole Normale Super, CNRS, UMR 8553, F-75005 Paris, France

[3] Ctr Altos Estudios Ciencia Exactas, RA-1084 Buenos Aires, DF, Argentina

关键词: Affine Kac-Moody Lie algebra;    Conjugacy;    Reductive group scheme;    Torsor;    Laurent polynomials;    Non-abelian cohomology;   

DOI  :  10.1016/j.jalgebra.2013.09.037

来源: Elsevier

【 摘 要 】

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. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free