A covering dimension for 𝐶*-algebras

Abstract

We introduce a notion of dimension for ð¶*-algebras that is a noncommutative version of the covering dimension for spaces, and study its basic properties and some properties for continuous field ð¶*-algebras, tensor products and composition series. As an application we estimate the dimension of the group ð¶*-algebras of some important solvable Lie groups.