Uniqueness Theorems and Ideal Structure for Leavitt Path Algebras
Operator Algebras
2007-05-23 v6 Rings and Algebras
Abstract
We prove Leavitt path algebra versions of the two uniqueness theorems of graph C*-algebras. We use these uniqueness theorems to analyze the ideal structure of Leavitt path algebras and give necessary and sufficient conditions for their simplicity. We also use these results to give a proof of the fact that for any graph E the Leavitt path algebra embeds as a dense *-subalgebra of the graph C*-algebra C*(E). This embedding has consequences for graph C*-algebras, and we discuss how we obtain new information concerning the construction of C*(E).
Cite
@article{arxiv.math/0612628,
title = {Uniqueness Theorems and Ideal Structure for Leavitt Path Algebras},
author = {Mark Tomforde},
journal= {arXiv preprint arXiv:math/0612628},
year = {2007}
}
Comments
34 pages, uses XY-pic. New version comments: Some small typos corrected. This is the final version to appear in the Journal of Algebra