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Search: All articles in the CJM digital archive with keyword free entropy

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1. CJM Online first

Graham, Robert; Pichot, Mikael
 A Free Product Formula for the Sofic Dimension It is proved that if \$G=G_1*_{G_3}G_2\$ is free product of probability measure preserving \$s\$-regular ergodic discrete groupoids amalgamated over an amenable subgroupoid \$G_3\$, then the sofic dimension \$s(G)\$ satisfies the equality \[ s(G)=\mathfrak{h}(G_1^0)s(G_1)+\mathfrak{h}(G_2^0)s(G_2)-\mathfrak{h}(G_3^0)s(G_3) \] where \$\mathfrak{h}\$ is the normalized Haar measure on \$G\$. Keywords:sofic groups, dynamical systems, orbit equivalence, free entropyCategory:20E06

2. CJM 2011 (vol 63 pp. 551)

Hadwin, Don; Li, Qihui; Shen, Junhao
 Topological Free Entropy Dimensions in Nuclear C\$^*\$-algebras and in Full Free Products of Unital C\$^*\$-algebras In the paper, we introduce a new concept, topological orbit dimension of an \$n\$-tuple of elements in a unital C\$^{\ast}\$-algebra. Using this concept, we conclude that Voiculescu's topological free entropy dimension of every finite family of self-adjoint generators of a nuclear C\$^{\ast}\$-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 C\$^{\ast}\$-algebras. We show that the unital full free product of Blackadar and Kirchberg's unital MF algebras is also an MF algebra. As an application, we obtain that \$\mathop{\textrm{Ext}}(C_{r}^{\ast}(F_{2})\ast_{\mathbb{C}}C_{r}^{\ast}(F_{2}))\$ is not a group. Keywords: topological free entropy dimension, unital C\$^{*}\$-algebraCategories:46L10, 46L54