Geodesic
Topological Free Entropy Dimensions in Nuclear C*-algebras and in Full Free Products of Unital C*-algebras
Canadian journal of mathematics, Tome 63 (2011) no. 3, pp. 551-590

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DOI

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.
DOI : 10.4153/CJM-2011-014-8
Mots-clés : 46L10, 46L54, topological free entropy dimension, unital C*-algebra 
Hadwin, Don; Li, Qihui; Shen, Junhao. Topological Free Entropy Dimensions in Nuclear C*-algebras and in Full Free Products of Unital C*-algebras. Canadian journal of mathematics, Tome 63 (2011) no. 3, pp. 551-590. doi: 10.4153/CJM-2011-014-8
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     author = {Hadwin, Don and Li, Qihui and Shen, Junhao},
     title = {Topological {Free} {Entropy} {Dimensions} in {Nuclear} {C*-algebras} and in {Full} {Free} {Products} of {Unital} {C*-algebras}},
     journal = {Canadian journal of mathematics},
     pages = {551--590},
     year = {2011},
     volume = {63},
     number = {3},
     doi = {10.4153/CJM-2011-014-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2011-014-8/}
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