On the \(K\)-theory of \(C^\ast\)-algebras associated with \(n\)-simplexes
J. Cuntz defined noncommutative \(C^\ast\)-algebras for simplicial (flag) complexes and related these to the Baum-Connes assembly map for a discrete group. These \(C^\ast\)-algebras have a rich ideal structure related to the combinatorics of the underlying simplicial complex. This leads to a filtration with less complicated subquotients and suggests a way to compute the \(K\)-theory of these \(C^\ast\)-algebras. This article computes the \(K\)-theory of some of these algebras and of some of their subquotients in this way. The methods are elementary.
scientific article; zbMATH DE number 6081050