The socle of a Leavitt path algebra

By G. Pino, D. M. Barquero, Cándido Martín González, Mercedes Siles Molina. 2007

58 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a712afa9d3be2ae6cc5d703569d3ee7625c548a6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Xiao-Wu Chen
2. Apostolos Beligiannis
3. P. Ara
4. Pu Zhang
5. Kulumani M. Rangaswamy

In Geometry and Topology

1. Xiao-Wu Chen
2. Apostolos Beligiannis
3. P. Ara
4. Pu Zhang
5. Kulumani M. Rangaswamy

In Mathematical Physics

1. Xiao-Wu Chen
2. Apostolos Beligiannis
3. P. Ara
4. Kulumani M. Rangaswamy

Citations in the corpus

• Irreducible representations of Leavitt path algebras (2011, methodology): “These representations are classified in [9, 10].”