Atlas of Leavitt path algebras of small graphs

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. [1] 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.