Conjugacy theorems for loop reductive group schemes and Lie algebras

• Autores: Chernousov, Vladimir; Gille, Philippe; Pianzola, Arturo
• Año de publicación: 2014
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: BUILDING; CONJUGACY; LAURENT POLYNOMIALS; LOOP REDUCTIVE GROUP SCHEME; NON-ABELIAN COHOMOLOGY; TORSOR
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

The conjugacy of split Cartan subalgebras in the finite-dimensional simple case (Chevalley) and in the symmetrizable Kac–Moody case (Peterson–Kac) are fundamental results of the theory of Lie algebras. Among the Kac–Moody Lie algebras the affine algebras stand out. This paper deals with the problem of conjugacy for a class of algebras—extended affine Lie algebras—that are in a precise sense higher nullity analogues of the affine algebras. Unlike the methods used by Peterson–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 Bruhat–Tits on buildings. The main ingredient of our conjugacy proof is the classification of loop torsors over Laurent polynomial rings, a result of its own interest.
Fil: Chernousov, Vladimir. University of Alberta; Canadá
Fil: Gille, Philippe. University of Alberta; Canadá
Fil: Pianzola, Arturo. Universidad Centro de Altos Estudios en Ciencia Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina