Commutator Leavitt path algebras
Rings and Algebras
2013-09-23 v1
Abstract
For any field K and directed graph E, we completely describe the elements of the Leavitt path algebra L_K(E) which lie in the commutator subspace [L_K(E),L_K(E)]. We then use this result to classify all Leavitt path algebras L_K(E) that satisfy L_K(E)=[L_K(E),L_K(E)]. We also show that these Leavitt path algebras have the additional (unusual) property that all their Lie ideals are (ring-theoretic) ideals, and construct examples of such rings with various ideal structures.
Keywords
Cite
@article{arxiv.1205.5319,
title = {Commutator Leavitt path algebras},
author = {Zachary Mesyan},
journal= {arXiv preprint arXiv:1205.5319},
year = {2013}
}
Comments
24 pages