Torsors, reductive group schemes and extended affine Lie algebras / Philippe Gille, Arturo Pianzola

Auteur: Gille, Philippe (1968-) - AuteurCo-auteur: Pianzola, Arturo (1955-) - AuteurType de document: MonographieCollection: Memoirs of the American Mathematical Society ; 1063Langue: anglaisPays: Etats UnisÉditeur: Providence (R.I.) : American Mathematical Society, 2013Description: 1 vol. (V-112 p.) ; 26 cm ISBN: 9780821887745 ; br. ISSN: 0065-9266Résumé: We give a detailed description of the torsors that correspond to multiloop algebras. These algebras are twisted forms of simple Lie algebras extended over Laurent polynomial rings. They play a crucial role in the construction of Extended Affine Lie Algebras (which are higher nullity analogues of the affine Kac-Moody Lie algebras). The torsor approach that we take draws heavily for the theory of reductive group schemes developed by M. Demazure and A. Grothendieck. It also allows us to find a bridge between multiloop algebras and the work of F. Bruhat and J. Tits on reductive groups over complete local fields..Bibliographie: Bibliogr. p. 109-112. Sujets MSC: 17B67 Nonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
11E72 Number theory -- Forms and linear algebraic groups -- Galois cohomology of linear algebraic groups
14L30 Algebraic geometry -- Algebraic groups -- Group actions on varieties or schemes (quotients)
14E20 Algebraic geometry -- Birational geometry -- Coverings
En-ligne: Hal | MathSciNet
Location Call Number Status Date Due
Couloir 12350-01 / Séries AMS (Browse Shelf) Available

Bibliogr. p. 109-112

We give a detailed description of the torsors that correspond to multiloop algebras. These algebras are twisted forms of simple Lie algebras extended over Laurent polynomial rings. They play a crucial role in the construction of Extended Affine Lie Algebras (which are higher nullity analogues of the affine Kac-Moody Lie algebras). The torsor approach that we take draws heavily for the theory of reductive group schemes developed by M. Demazure and A. Grothendieck. It also allows us to find a bridge between multiloop algebras and the work of F. Bruhat and J. Tits on reductive groups over complete local fields.

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