The socle of a Leavitt path algebra

• Autores: Gonzalo Aranda Pino , Dolores Martín Barquero , Cándido Martín González , Mercedes Siles Molina
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 212, Nº 3, 2008, págs. 500-509
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2007.06.001
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• Resumen

  • In this paper we characterize the minimal left ideals of a Leavitt path algebra as those which are isomorphic to principal left ideals generated by line points; that is, by vertices whose trees contain neither bifurcations nor closed paths. Moreover, we show that the socle of a Leavitt path algebra is the two-sided ideal generated by these line point vertices. This characterization allows us to compute the socle of certain algebras that arise as the Leavitt path algebra of a row-finite graph. A complete description of the socle of a Leavitt path algebra is given: it is a locally matricial algebra.