Simple Lie algebras arising from Leavitt path algebras
Rings and Algebras
2012-07-12 v2
Abstract
For a field K and directed graph E, we analyze those elements of the Leavitt path algebra L_K(E) which lie in the commutator subspace [L_K(E), L_K(E)]. This analysis allows us to give easily computable necessary and sufficient conditions to determine which Lie algebras of the form [L_K(E), L_K(E)] are simple, when E is row-finite (i.e., has finite out-degree) and L_K(E) is simple.
Cite
@article{arxiv.1107.3114,
title = {Simple Lie algebras arising from Leavitt path algebras},
author = {Gene Abrams and Zachary Mesyan},
journal= {arXiv preprint arXiv:1107.3114},
year = {2012}
}
Comments
18 pages. In the second version the exposition has been improved, and various typos and minor errors have been corrected