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

## TL;DR

This paper computes the topological free entropy dimension for individual self-adjoint elements and families of generators in unital C*-algebras, providing new insights into their structural properties.

## Contribution

It introduces explicit calculations of topological free entropy dimensions for specific elements and classes of unital C*-algebras, expanding understanding of their entropy characteristics.

## Key findings

- Computed topological free entropy dimension of one self-adjoint element.
- Calculated topological orbit dimension of one self-adjoint element.
- Determined entropy dimensions for generators of irrational rotation and free group tensor product C*-algebras.

## Abstract

The notion of topological free entropy dimension of $n-$tuples of elements in a unital C$^*$ 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$^*$ algebra. Moreover, we calculate the values of topological free entropy dimensions of families of generators of some unital C$^*$ algebras (for example: irrational rotation C$^*$ algebras or minimal tensor product of two reduced C$^*$ algebras of free groups).