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The regular algebra of a quiver

Pere Ara·Miquel Brustenga
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Abstract

Let $K$ be a fixed field. We attach to each column-finite quiver $E$ a von Neumann regular $K$-algebra $Q(E)$ in a functorial way. The algebra $Q(E)$ is a universal localization of the usual path algebra $P(E)$ associated with $E$. The monoid of isomorphism classes of finitely generated projective right $Q(E)$-modules is explicitly computed.

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Pere Ara, Miquel Brustenga. 2006-05-05. The regular algebra of a quiver. https://arxiv.org/abs/math/0605151

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