Torsors, reductive group schemes and extended affine Lie algebras

Philippe Gille, Arturo Pianzola

Type: Article

Publication Date: 2013-01-01

Citations: 21

DOI: https://doi.org/10.1090/s0065-9266-2013-00679-x

Abstract

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 J. Tits on reductive groups over complete local fields.

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Works Cited by This (69)

Action	Title	Year	Authors
+	Torseurs sur la droite affine et R-équivalence	1994	Philippe Gille
+	Groupes algébriques sur un corps local: III. Compléments et applications à la cohomologie galoisienne	1987	François Bruhat Jacques Tits
+	Central Simple Algebras and Galois Cohomology	2006	Philippe Gille Tamás Szamuely
+	Unipotent subgroups of reductive groups in characteristic $p > 0$	2002	Philippe Gille
+	Pseudo-reductive Groups	2010	Brian Conrad Ofer Gabber Gopal Prasad
+	Quadratic and Hermitian Forms over Rings	1991	Max-Albert Knus
+	Linear algebraic groups	1966	Armand Borel
+	Lie groups and algebraic groups	1990	É. B. Vinberg A. L. Onishchik Dimitry Leites
+	Serre’s Problem on Projective Modules	2006	Tsit Yuen Lam
+	Cohomology of Number Fields	2008	Jürgen Neukirch Alexander Schmidt Kay Wingberg