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

Academic Article


  • 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.
  • Authors

  • Hadwin, Don
  • Li, Qihui
  • Shen, Junhao
  • Status

    Publication Date

  • June 2011
  • Has Subject Area

    Published In


  • topological free entropy dimension
  • unital C*-algebra
  • Digital Object Identifier (doi)

    Start Page

  • 551
  • End Page

  • 590
  • Volume

  • 63
  • Issue

  • 3