\(C^*\)-algebras, Gelfand-Kirillov dimension, and Følner sets
It is shown that the set of asymptotic growth types of a finitely generated \(C^*\)-algebra is either completely polynomial, completely exponential, or mixed while containing exponential growth types. Further, it is shown that a finitely generated \(C^*\)-algebra has only completely polynomial growth types if and only if, for some \(n\in{\mathbb{N}}\), it can be imbedded into the algebra of \(n\times n\) matrices over a commutative \(C^*\)-algebra. Some of the results are extended to non finitely generated \(C^*\)-algebras.
scientific article; zbMATH DE number 1437357
scientific article