Topological Free Entropy Dimension of in Unital C^*-algebras

Abstract

The notion of topological free entropy dimension of $n-$tuples of elements in a unital C${}^{\ast }$ algebra was introduced by Voiculescu. In the paper, we compute topological free entropy dimension of one self-adjoint element and topological orbit dimension of one self-adjoint element in a unital C${}^{\ast }$ algebra. Moreover, we calculate the values of topological free entropy dimensions of families of generators of some unital C${}^{\ast }$ algebras (for example: irrational rotation C${}^{\ast }$ algebras or minimal tensor product of two reduced C${}^{\ast }$ algebras of free groups).

Materials added