$C^{\ast }$-algebras generated by the paths semigroup

Abstract

In this paper we study the structure of the $C^{\ast }$-algebra, generated by the representation of the paths semigroup on a partially ordered set (poset) and get the net of isomorphic $C^{\ast }$-algebras over this poset. We construct the extensions of this algebra, such that the algebra is an ideal in that extensions and quotient algebras are isomorphic to the Cuntz algebra.

12 pages