The K-theory ranks for crossed products of C*-algebras by the group of integers

Abstract

We study the K-theory ranks for crossed products of C∗-algebras by the group of integers. As an application, we obtain certain estimates for the K-theory ranks of the group C∗-algebras of torsion free, finitely generated, nilpotent or solvable discrete groups, written as successive semi-direct products.

Keywords

• k-theory
• c*-algebra
• crossed product
• betti number
• discrete group