C*-algebra generated by the paths semigroup

Abstract

In this paper we study the structure of the C*-algebra, generated by the representation of the paths semigroup on a partially ordered set (poset) and get the net of isomorphic C*-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.