Topological Free Entropy Dimensions in Nuclear C*-algebras and in Full Free Products of Unital C*-algebras

Hadwin, Don ; Li, Qihui ; Shen, Junhao

Canadian journal of mathematics, Tome 63 (2011) no. 3, pp. 551-590

Résumé

In the paper, we introduce a new concept, topological orbit dimension of an $n$ -tuple of elements in a unital ${{\text{C}}^{*}}$ -algebra. Using this concept, we conclude that Voiculescu's topological free entropy dimension of every finite family of self-adjoint generators of a nuclear ${{\text{C}}^{*}}$ -algebra is less than or equal to 1. We also show that the Voiculescu's topological free entropy dimension is additive in the full free product of some unital ${{\text{C}}^{*}}$ -algebras. We show that the unital full free product of Blackadar and Kirchberg's unital $\text{MF}$ algebras is also an $\text{MF}$ algebra. As an application, we obtain that $\text{Ext(}C_{r}^{*}\text{(}{{F}_{2}}\text{)}{{\text{*}}_{\mathbb{C}}}C_{r}^{*}\text{(}{{F}_{2}}\text{))}$ is not a group.

Détail

DOI : 10.4153/CJM-2011-014-8

Mots-clés : 46L10, 46L54, topological free entropy dimension, unital C*-algebra

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