Revista Matemática Iberoamericana

Socle theory for Leavitt path algebras of arbitrary graphs

Gonzalo Aranda Pino , Dolores Martín Barquero , Cándido Martín González , and Mercedes Siles Molina

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Abstract

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.

Article information

Source
Rev. Mat. Iberoamericana, Volume 26, Number 2 (2010), 611-638.

Dates
First available in Project Euclid: 4 June 2010

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1275671313

Mathematical Reviews number (MathSciNet)
MR2677009

Zentralblatt MATH identifier
1203.16013

Subjects
Primary: 16D70: Structure and classification (except as in 16Gxx), direct sum decomposition, cancellation

Keywords
Leavitt path algebra graph C*-algebra socle arbitrary graph minimal left ideal

Citation

Aranda Pino, Gonzalo; Martín Barquero, Dolores; Martín González, Cándido; Siles Molina, Mercedes. Socle theory for Leavitt path algebras of arbitrary graphs. Rev. Mat. Iberoamericana 26 (2010), no. 2, 611--638. https://projecteuclid.org/euclid.rmi/1275671313


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