The Realization Problem for Finitely Generated Refinement Monoids

Autor:	Ara, Pere, Bosa, Joan, Pardo, Enrique
Rok vydání:	2019
Předmět:	Mathematics - Rings and Algebras Mathematics - Functional Analysis Mathematics - Operator Algebras 16D70 16E50 06F20 19K14 20K20 46L05
Druh dokumentu:	Working Paper
Popis:	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 $Q_K (E, C)$ and show that there is a natural isomorphism between the separated graph monoid $M(E, C)$ and the monoid $\mathcal V(Q_K (E, C))$. Comment: Final version, accepted for publication in Selecta Mathematica
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1907.03648 Zobrazit plný text záznamu View this record from Arxiv