The Automorphism Group of a Simple Tracially Ai Algebra
نویسندگان
چکیده
The structure of the automorphism group of a simple TAI algebra is studied. In particular, we show that Inn(A) Inn0(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, Inn(A) Inn0(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 (T, hn) with a unique hn-invariant probability measure on T . Then the automorphism group of A is an extension of a simple topological group by the discrete group Aut(K(A))+,1.
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