The socle of a Leavitt path algebra

被引：36

作者：

Pino, G. Aranda ^{[1
]}

Barquero, D. Martfn ^{[2
]}

Gonzalez, C. Martin ^{[3
]}

Molina, M. Siles ^{[3
]}

机构：

[1] Ctr Rech Math, E-08193 Barcelona, Spain

[2] Univ Malaga, Dept Matemat Aplicada, E-29071 Malaga, Spain

[3] Univ Malaga, Dept Algebra Geometria & Topol, E-29071 Malaga, Spain

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2008年 / 212卷 / 03期

关键词：

D O I：

10.1016/j.jpaa.2007.06.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (c) 2007 Elsevier B.V. All rights reserved.

引用

页码：500 / 509

页数：10

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