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arXiv · 2012.11191

Lie nilpotent Novikov algebras and Lie solvable Leavitt path algebras

Zerui Zhang·Tran Giang Nam
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Abstract

In this paper, we first study properties of the lower central chains for Novikov algebras. Then we show that for every Lie nilpotent Novikov algebra~$\mathcal{N}$, the ideal of~$\mathcal{N}$ generated by the set~$\{ab - ba\mid a, b\in \mathcal{N}\}$ is nilpotent. We secondly provide necessary and sufficient conditions on the graph $E$ and the field $K$ for which the Leavitt path algebra $L_K(E)$ is Lie solvable. Consequently, we obtain a complete description of Lie nilpotent Leavitt path algebras, and show that the Lie solvability of~$L_K(E)$ and the Lie nilpotency of $[L_K(E),L_K(E)]$ are the same.

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Zerui Zhang, Tran Giang Nam. 2020-12-21. Lie nilpotent Novikov algebras and Lie solvable Leavitt path algebras. https://arxiv.org/abs/2012.11191

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