Socle theory for Leavitt path algebras of arbitrary graphs
By G. Pino, D. M. Barquero, Cándido Martín González, Mercedes Siles Molina. Revista matemática iberoamericana, 2008
73 citations recorded by the source corpus.
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 Leavit t path algebra, extending so the results for row-finite graphs in the previous paper (12) ( but with different methods). A concrete description of the socle of a Leavitt path algebra i s 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, shorthening significantly the original ones.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d83601718a9bfaf86c548e01c68ca0fa88efde8e
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Citations in the corpus
- Finitely presented simple modules over Leavitt path algebras (2013, background): “ule. Obviously we have J ∩ F0 = ∅, because every vertex in F connects to w. On the other hand, F satisfies condition (L) as every vertex in F connects to the sink w and this means, by Proposition 1 of [14], that every non-zero ideal of L(F) contains a vertex. Consequently, J = 0. This proves the resu”