A Talented Monoid View on Lie Bracket Algebras over Leavitt Path Algebras
Rings and Algebras
2022-03-24 v1 Group Theory
Abstract
In this article, we study properties as simplicity, solvability and nilpotency for Lie bracket algebras arising from Leavitt path algebras, based on the talented monoid of the underlying graph. We show that graded simplicity and simplicity of the Leavitt path algebra can be connected via the Lie bracket algebra. Moreover, we use the Gelfand-Kirillov dimension for the Leavitt path algebra for a classification of nilpotency and solvability.
Keywords
Cite
@article{arxiv.2203.04047,
title = {A Talented Monoid View on Lie Bracket Algebras over Leavitt Path Algebras},
author = {Wolfgang Bock and Alfilgen Sebandal and Jocelyn Viliela},
journal= {arXiv preprint arXiv:2203.04047},
year = {2022}
}