Abstract: In this article we introduce a universal C (∗)-algebras associated to certain simplicial flag complexes. We denote it by [Formula: see text]it is a subalgebra of the noncommutative n-sphere which introduced by J.Cuntz. We present a technical lemma to determine the quotient of the skeleton filtration of a general universal C (∗)-algebra associated to a simplicial flag complex. We examine the K-theory of this algebra. Moreover we prove that any such algebra divided by the ideal I 2 is commutative.
2000 ams: 19 K 46.
Keywords: K- theory of C∗-algebras; Universal C∗-algebras; Simplicial complexes.