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arXiv · 2606.20288

Free subgroups in weighted Leavitt Path Algebras

Huynh Viet Khanh
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Abstract

We study unit groups of weighted Leavitt path algebras. Let $K$ be a field of characteristic $0$ and let $(E,\omega)$ be a finite connected weighted graph. We prove that $L_K(E,\omega)^\times$ is abelian if and only if $L_K(E,\omega)$ is a domain. Equivalently, $L_K(E,\omega)^\times$ contains no non-cyclic free subgroup if and only if $L_K(E,\omega)$ is a domain.

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Huynh Viet Khanh. 2026-06-18. Free subgroups in weighted Leavitt Path Algebras. https://arxiv.org/abs/2606.20288

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