scholarly journals Free entropy dimension in amalgamated free products

2008 ◽  
Vol 97 (2) ◽  
pp. 339-367 ◽  
Author(s):  
Nathanial P. Brown ◽  
Kenneth J. Dykema ◽  
Kenley Jung
Keyword(s):  
Free Products ◽  
Free Entropy ◽  
Amalgamated Free Products ◽  
Entropy Dimension ◽  
Free Entropy Dimension

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

2011 ◽  
Vol 63 (3) ◽  
pp. 551-590 ◽  
Author(s):  
Don Hadwin ◽  
Qihui Li ◽  
Junhao Shen
Keyword(s):  
Free Product ◽  
Finite Family ◽  
Free Products ◽  
C Algebra ◽  
Free Entropy ◽  
C Algebras ◽  
Entropy Dimension ◽  
Free Entropy Dimension

Abstract In the paper, we introduce a new concept, topological orbit dimension of an n-tuple of elements in a unital 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 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 C*-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 Ext(C*r (F2) *C C* r (F2)) is not a group.

scholarly journals Free entropy dimension and regularity of non-commutative polynomials

2016 ◽  
Vol 271 (8) ◽  
pp. 2274-2292 ◽  
Author(s):  
Ian Charlesworth ◽  
Dimitri Shlyakhtenko
Keyword(s):  
Free Entropy ◽  
Entropy Dimension ◽  
Free Entropy Dimension

FREE ENTROPY DIMENSION OF PROJECTIONS AND FACTORIALITY OF GENERATED VON NEUMANN ALGEBRAS

2008 ◽  
Vol 11 (02) ◽  
pp. 295-305
Author(s):  
TAKUHO MIYAMOTO
Keyword(s):  
Von Neumann Algebra ◽  
Von Neumann Algebras ◽  
Sufficient Condition ◽  
Von Neumann ◽  
Free Entropy ◽  
Entropy Dimension ◽  
Free Entropy Dimension

We examine the free entropy and free entropy dimension for projections, and obtain a sufficient condition for the factoriality of the von Neumann algebra generated by projections in terms of their free entropy dimension. This corresponds to Voiculescu's result for self-adjoint elements.

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