Leavitt path algebras of labelled graphs
Rings and Algebras
2021-06-14 v1 Operator Algebras
Abstract
A Leavitt labelled path algebra over a commutative unital ring is associated with a labelled space, generalizing Leavitt path algebras associated with graphs and ultragraphs as well as torsion-free commutative algebras generated by idempotents. We show that Leavitt labelled path algebras can be realized as partial skew group rings, Steinberg algebras, and Cuntz-Pimsner algebras. Via these realizations we obtain generalized uniqueness theorems, a description of diagonal preserving isomorphisms and we characterize simplicity of Leavitt labelled path algebras. In addition, we prove that a large class of partial skew group rings can be realized as Leavitt labelled path algebras.
Keywords
Cite
@article{arxiv.2106.06036,
title = {Leavitt path algebras of labelled graphs},
author = {Giuliano Boava and Gilles G. de Castro and Daniel Gonçalves and Daniel W. van Wyk},
journal= {arXiv preprint arXiv:2106.06036},
year = {2021}
}