Torsors, reductive group schemes and extended affine Lie algebras

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...

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Detalhes bibliográficos
Autores: Gille, Philippe, Pianzola, Arturo
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2013
País:Argentina
Recursos:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/25470
Acesso em linha:http://hdl.handle.net/11336/25470
Access Level:acceso abierto
Palavra-chave:Reductive Group Schemes
Loop Torsors
Extended Affine Lie Algebras
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descrição
Resumo: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.