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The socle of a Leavitt path algebra by G. Aranda Pino; D. Martín Barquero; C. Martín González; M. Siles Molina is a Mathematics article available to read on EtoBox.

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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.

Who reads The socle of a Leavitt path algebra?

Author

G. Aranda Pino; D. Martín Barquero; C. Martín González; M. Siles Molina

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0022-4049)

Published

2008

Language

EN

Field

Mathematics (Physical Sciences)