Communications in Mathematical Physics

, Volume 280, Issue 2, pp 427–444 | Cite as

The Automorphism Group of a Simple Tracially AI Algebra

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Abstract

The structure of the automorphism group of a simple TAI algebra is studied. In particular, we show that \({\frac{\overline{ \rm{Inn}}(A) }{ \overline{\rm{Inn}}_{0} ( A ) }}\) is isomorphic (as a topological group) to an inverse limit of discrete abelian groups for a unital, simple, AH algebra with bounded dimension growth. Consequently, \({\frac{\overline{\rm{Inn}}(A)}{\overline{\rm{Inn}}_{0}(A) }}\) is totally disconnected.

Another consequence of our results is the following: Suppose A is the transformation group C*-algebra of a minimal Furstenberg transformation with a unique invariant probability measure. Then the automorphism group of A is an extension of a simple topological group by the discrete group \({\rm{Aut}(\underline{K}(A))_{+,1}}\).

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© Springer-Verlag 2008

Authors and Affiliations

  1. 1.University of Louisiana at LafayetteLafayetteUSA
  2. 2.Department of MathematicsUniversity of Hawaii HiloHiloUSA

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