A note on Lie and Jordan structures of Leavitt path algebras

Huynh Viet Khanh; Le Qui Danh

doi:10.1142/S0219498827501568

A note on Lie and Jordan structures of Leavitt path algebras

Rings and Algebras 2026-02-27 v2

Authors: Huynh Viet Khanh , Le Qui Danh

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Abstract

Let $L_K(E)$ be the Leavitt path algebra of a directed graph $E$ over a field $K$ . In this paper, we determine $E$ and $K$ for the Lie algebra $\mathbf{K}_{L_K(E)}$ and the Jordan algebra $\mathbf{S}_{L_K(E)}$ arising from $L_K(E)$ with respect to the standard involution to be solvable.

Keywords

Leavitt path algebra Lie algebra Jordan algebra solvable algebra standard involution

Cite

@article{arxiv.2503.19277,
  title  = {A note on Lie and Jordan structures of Leavitt path algebras},
  author = {Huynh Viet Khanh and Le Qui Danh},
  journal= {arXiv preprint arXiv:2503.19277},
  year   = {2026}
}

Comments

Accepted for publication on JAA

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