The groupoid approach to Leavitt path algebras
Abstract
When the theory of Leavitt path algebras was already quite advanced, it was discovered that some of the more difficult questions were susceptible to a new approach using topological groupoids. The main result that makes this possible is that the Leavitt path algebra of a graph is graded isomorphic to the Steinberg algebra of the graph's boundary path groupoid. This expository paper has three parts: Part 1 is on the Steinberg algebra of a groupoid, Part 2 is on the path space and boundary path groupoid of a graph, and Part 3 is on the Leavitt path algebra of a graph. It is a self-contained reference on these topics, intended to be useful to beginners and experts alike. While revisiting the fundamentals, we prove some results in greater generality than can be found elsewhere, including the uniqueness theorems for Leavitt path algebras.
Cite
@article{arxiv.1811.02269,
title = {The groupoid approach to Leavitt path algebras},
author = {Simon W. Rigby},
journal= {arXiv preprint arXiv:1811.02269},
year = {2019}
}
Comments
Thanks to T.G. Nam for helping to resolve an error in Theorem 2.4 of the earlier version. To appear in Proceedings of the International Workshop on Leavitt Path Algebras and K-Theory