Atlas of Leavitt Path Algebras of small graphs
Rings and Algebras
2011-12-30 v1
Abstract
The aim of this work is the description of the isomorphism classes of all Leavitt path algebras coming from graphs satisfying Condition (Sing) with up to three vertices. In particular, this classification recovers the one achieved by Abrams et al. in the case of graphs whose Leavitt path algebras are purely infinite simple. The description of the isomorphism classes is given in terms of a series of invariants including the K_0 group, the socle, the number of loops with no exits and the number of hereditary and saturated subsets of the graph.
Keywords
Cite
@article{arxiv.1112.5735,
title = {Atlas of Leavitt Path Algebras of small graphs},
author = {Pablo Alberca Bjerregaard and Gonzalo Aranda Pino and Dolores Martín Barquero and Cándido Martín González and Mercedes Siles Molina},
journal= {arXiv preprint arXiv:1112.5735},
year = {2011}
}