Associative and Lie algebras of quotients

In this paper we examine how the notion of algebra of quotients for Lie algebras ties up with the corresponding well-known concept in the associative case. Specifically, we completely characterize when a Lie algebra Q is an algebra of quotients of a Lie algebra L in terms of the associative algebras...

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Detalles Bibliográficos
Autores: Perera Domènech, Francesc|||0000-0002-4669-4736, Siles Molina, Mercedes|||0000-0002-4299-5187
Tipo de recurso: artículo
Fecha de publicación:2008
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:21994
Acceso en línea:https://ddd.uab.cat/record/21994
https://dx.doi.org/urn:doi:10.5565/PUBLMAT_52108_06
Access Level:acceso abierto
Palabra clave:Lie algebra
Algebra of quotients
Multiplicative semiprime algebra
Dense extension
Descripción
Sumario:In this paper we examine how the notion of algebra of quotients for Lie algebras ties up with the corresponding well-known concept in the associative case. Specifically, we completely characterize when a Lie algebra Q is an algebra of quotients of a Lie algebra L in terms of the associative algebras generated by the adjoint operators of L and Q respectively. In a converse direction, we also provide with new examples of algebras of quotients of Lie algebras and these come from associative algebras of quotients. In the course of our analysis, we make use of the notions of density and multiplicative semiprimeness to link our results with the maximal symmetric ring of quotients.