The regular algebra of a poset

Abstract

Let $K$ be a field. We attach to each finite poset $\mathbb{P}$ a von Neumann regular $K$-algebra $Q_K(\mathbb{P})$ in a functorial way. We show that the monoid of isomorphism classes of finitely generated projective $Q_K(\mathbb{P})$-modules is the abelian monoid generated by $\mathbb{P}$ with the only relations given by $p=p+q$ whenever $q<p$ in $\mathbb{P}$. This extends the class of monoids for which there is a positive solution to the realization problem for von Neumann regular rings.

47 pages. Revised version, to appear in Trans. Amer. Math. Soc

References in corpus (2)

• The realization problem for von Neumann regular rings
• Mixed quiver algebras

Cited by in corpus (2)

• Mixed quiver algebras
• Representation of artinian partially ordered sets over semiartinian Von Neumann regular algebras