Memoirs of the American Mathematical Society 2013; 112 pp; softcover Volume: 226 ISBN10: 0821887742 ISBN13: 9780821887745 List Price: US$73 Individual Members: US$43.80 Institutional Members: US$58.40 Order Code: MEMO/226/1063
 The authors 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 KacMoody Lie algebras). The torsor approach that the authors take draws heavily from the theory of reductive group schemes developed by M. Demazure and A. Grothendieck. It also allows the authors to find a bridge between multiloop algebras and the work of F. Bruhat and J. Tits on reductive groups over complete local fields. Table of Contents  Introduction
 Generalities on the algebraic fundamental group, torsors, and reductive group schemes
 Loop, finite and toral torsors
 Semilinear considerations
 Maximal tori of group schemes over the punctured line
 Internal characterization of loop torsors and applications
 Isotropy of loop torsors
 Acyclicity
 Small dimensions
 The case of orthogonal groups
 Groups of type \(G_2\)
 Case of groups of type \(F_4,\) \(E_8\) and simply connected \(E_7\) in nullity \(3\)
 The case of \(\mathbf{PGL}_d\)
 Invariants attached to EALAs and multiloop algebras
 Appendix 1: Pseudoparabolic subgroup schemes
 Appendix 2: Global automorphisms of \(G\)torsors over the projective line
 Bibliography
