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	Título: Torsors, Reductive Group Schemes And Extended Affine Lie Algebras
	Autor: Philippe Gille, Ecole Normale Supérieure, Paris, France, An	Precio: Desconocido
	Editorial: American Mathematical Society	Año: 2013
	Tema:	Edición: 2ª
	Sinopsis	ISBN: 9780821887745
	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 Kac-Moody 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 G2 Case of groups of type F4, E8 and simply connected E7 in nullity 3 The case of PGLd Invariants attached to EALAs and multiloop algebras Appendix 1: Pseudo-parabolic subgroup schemes Appendix 2: Global automorphisms of G-torsors over the projective line Bibliography

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