2007/01/23 by Gonzalo Aranda Pino, Dolores Martı́n Barquero, Pino, Gonzalo Aranda +5
Mathematics · Physics and Astronomy · #16D70 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.math/0701637
openalex publication_date 2007/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 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.