The regular algebra of a quiver

2006/05/05 by Pere Ara, Ara, Pere, Miquel Brustenga +1
Mathematics · #16E50 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16E50

paper · pdf · doi:10.48550/arxiv.math/0605151

29 pages

arxiv created 2006/05/05 · arxiv updated 2009/12/01

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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