The regular algebra of a poset

Let K be a fixed 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 relat...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2010-03, Vol.362 (3), p.1505-1546
Main Author: ARA, PERE
Format: Article
Language:English
Subjects:
Algebra
Exact sciences and technology
Functional analysis
Homomorphisms
Mathematical analysis
Mathematical rings
Mathematical theorems
Mathematics
Monoids
Morphisms
Partial differential equations
Partially ordered sets
Sciences and techniques of general use
Vertices
Von Neumann algebra
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Summary:Let K be a fixed 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
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-09-04884-3