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arXiv · 2002.06965

Strongly graded Leavitt path algebras

Patrik Lundström·Johan Öinert
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Abstract

Let $R$ be a unital ring, let $E$ be a directed graph and recall that the Leavitt path algebra $L_R(E)$ carries a natural $\mathbb{Z}$-gradation. We show that $L_R(E)$ is strongly $\mathbb{Z}$-graded if and only if $E$ is row-finite, has no sink, and satisfies Condition (Y). Our result generalizes a recent result by Clark, Hazrat and Rigby, and the proof is short and self-contained.

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Patrik Lundström, Johan Öinert. 2020-02-17. Strongly graded Leavitt path algebras. https://arxiv.org/abs/2002.06965

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