The socle of a Leavitt path algebra

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dc.creatorPino, Gonzalo Aranda
dc.creatorBarquero, Dolores Martin
dc.creatorGonzalez, Candido Martin
dc.creatorMolina, Mercedes Siles
dc.date2007-01-23
dc.date.accessioned2026-07-07T07:42:40Z
dc.date.available2026-07-07T07:42:40Z
dc.descriptionIn this paper we characterize the minimal left ideals of a Leavitt path algebra as those ones which are isomorphic to principal left ideals generated by line point vertices, that is, by vertices whose trees do not 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 some algebras that arise as the Leavitt path algebra of some row-finite graphs. A complete description of the socle of a Leavitt path algebra is given: it is a locally matricial algebra.
dc.description13 pgs
dc.identifierhttps://arxiv.org/abs/math/0701637
dc.identifierhttp://arxiv.org/abs/math/0701637
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/122525
dc.subjectRings and Algebras
dc.subject16D70
dc.titleThe socle of a Leavitt path algebra
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