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arXiv · 2208.04739

The graded structure of Leavittt path algebras viewed as partial skew group rings

Daniel Gonçalves·Laura Orozco·Héctor Pinedo
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Abstract

Let $E$ be a directed graph, $\mathbb K$ be a field, and $\mathbb F$ be the free group on the edges of $E$. In this work, we use the isomorphism between Leavitt path algebras and partial skew group rings to endow $L_{\mathbb K}(E)$ with an $\mathbb F$-gradation and study some algebraic properties of this gradation. More precisely, we show that graded cleanness, graded unit-regularity, and strong gradeness of $L_{\mathbb K}(E)$ are all equivalent.

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Daniel Gonçalves, Laura Orozco, Héctor Pinedo. 2022-08-09. The graded structure of Leavittt path algebras viewed as partial skew group rings. https://arxiv.org/abs/2208.04739

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