  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.

Rings and Algebras;Algebraic Geometry;Representation Theory