On freely generated semigraph $C^{\ast }$-algebras

Abstract

For special universal $C^{\ast }$-algebras associated to $k$-semigraphs we present the universal representations of these algebras, prove a Cuntz--Krieger uniqueness theorem, and compute the $K$-theory. These $C^{\ast }$-algebras seem to be the most universal Cuntz--Krieger like algebras naturally associated to $k$-semigraphs. For instance, the Toeplitz Cuntz algebra is a proper quotient of such an algebra.

References in corpus (3)

• Higher rank graph C*-algebras
• Product systems of graphs and the Toeplitz algebras of higher-rank graphs
• C*-algebras of labelled graphs