A note on Lie and Jordan structures of Leavitt path algebras

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.

Publication Details

Journal
ArXiv.org
Published
2025-03-25
Primary Topic
Advanced Topics in Algebra
Type
article
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A note on Lie and Jordan structures of Leavitt path algebras

ArXiv.org
Advanced Topics in Algebra
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A note on Lie and Jordan structures of Leavitt path algebras

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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.

ArXiv.org
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Advanced Topics in Algebra
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A note on Lie and Jordan structures of Leavitt path algebras · ArXiv.org (2025) | TGRS Research Map | TGRS