Strongly graded Leavitt path algebras

@article{Nystedt2020StronglyGL,
  title={Strongly graded Leavitt path algebras},
  author={P. Nystedt and Johan Oinert},
  journal={arXiv: Rings and Algebras},
  year={2020}
}
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. 
2 Citations
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Elements of mathematics
Elements of Mathematics: Theory of Sets
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