The socle of a Leavitt path algebra
Rings and Algebras
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0701637,
title = {The socle of a Leavitt path algebra},
author = {Gonzalo Aranda Pino and Dolores Martin Barquero and Candido Martin Gonzalez and Mercedes Siles Molina},
journal= {arXiv preprint arXiv:math/0701637},
year = {2007}
}
Comments
13 pgs