Strongly graded Leavitt path algebras

Patrik Lundström; Johan Öinert

Strongly graded Leavitt path algebras

Rings and Algebras 2021-01-21 v3 Operator Algebras

Authors: Patrik Lundström , Johan Öinert

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.

Keywords

leavitt path algebras graded algebras

Cite

@article{arxiv.2002.06965,
  title  = {Strongly graded Leavitt path algebras},
  author = {Patrik Lundström and Johan Öinert},
  journal= {arXiv preprint arXiv:2002.06965},
  year   = {2021}
}

Comments

9 pages. Version 3: Minor improvements. Updated the last name of the first author

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