The Automorphism Group of a Simple Tracially AI Algebra期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

The Automorphism Group of a Simple Tracially AI Algebra

Authors:	Ping Wong Ng Efren Ruiz

Affiliation:	(1) University of Louisiana at Lafayette, 217 Maxim D. Doucet Hall, P.O. Box 41010, Lafayette, LA 70504-1010, USA;(2) Department of Mathematics, University of Hawaii Hilo, 200 W. Kawili St., Hilo, Hawaii 96720, USA

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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