The main aim of the paper is to give a socle theory for Leavitt
path algebras of arbitrary graphs. We use both the
desingularization process and combinatorial methods to study
Morita invariant properties concerning the socle and to
characterize it, respectively. Leavitt path algebras with nonzero
socle are described as those which have line points, and it is
shown that the line points generate the socle of a Leavitt path
algebra. A concrete description of the socle of a Leavitt path
algebra is obtained: it is a direct sum of matrix rings (of finite
or infinite size) over the base field.
New proofs of the Graded Uniqueness and of the Cuntz-Krieger
Uniqueness Theorems are given, by using very different means.
Publié le : 2010-06-15
Classification:
Leavitt path algebra,
graph C*-algebra,
socle,
arbitrary graph,
minimal left ideal,
16D70
@article{1275671313,
author = {Aranda Pino
,
Gonzalo and Mart\'\i n Barquero
,
Dolores and Mart\'\i n Gonz\'alez
,
C\'andido and Siles Molina
,
Mercedes},
title = {Socle theory for Leavitt path algebras of arbitrary graphs},
journal = {Rev. Mat. Iberoamericana},
volume = {26},
number = {1},
year = {2010},
pages = { 611-638},
language = {en},
url = {http://dml.mathdoc.fr/item/1275671313}
}
Aranda Pino
,
Gonzalo; Martín Barquero
,
Dolores; Martín González
,
Cándido; Siles Molina
,
Mercedes. Socle theory for Leavitt path algebras of arbitrary graphs. Rev. Mat. Iberoamericana, Tome 26 (2010) no. 1, pp. 611-638. http://gdmltest.u-ga.fr/item/1275671313/