2019/07/08 by Ara, Pere, Bosa, Joan, Pardo, Enrique
#06F20 #16D70 #16E50 #19K14 #20K20 #46L05 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1907.03648
We show that every finitely generated conical refinement monoid can be represented as the monoid \mathcal V(R) of isomorphism classes of finitely generated projective modules over a von Neumann regular ring R. To this end, we use the representation of these monoids provided by adaptable separated graphs. Given an adaptable separated graph (E, C) and a field K, we build a von Neumann regular K-algebra QK (E, C) and show that there is a natural isomorphism between the separated graph monoid M(E, C) and the monoid \mathcal V(QK (E, C)).