The regular algebra of a quiver

Details The regular algebra of a quiver The regular algebra of a quiver

2006-05-05

arxiv.org/abs/math/0605151v1

Mathematics

Rings and Algebras

29 pages

Scientific paper

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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