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arxiv: 2002.06965 · v3 · pith:GN74FGHYnew · submitted 2020-02-17 · 🧮 math.RA · math.OA

Strongly graded Leavitt path algebras

Patrik Lundstr\"om , Johan \"Oinert This is my paper
classification 🧮 math.RA math.OA
keywords gradedleavittmathbbpathresultstronglyalgebraalgebras
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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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    A modified fundamental theorem for algebraic K-theory is established for strongly Z-graded rings, with splittings via shift actions on modules and nil groups identified as reduced K-theory of homotopy nilpotent twiste...