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On Certain K-Groups Associated with Minimal Flows

Published online by Cambridge University Press:  20 November 2018

Jingbo Xia
Jingbo Xia*
Affiliation:
Department of Mathematics State University of New York at Buffalo Buffalo, New York 14214 U.S.A.
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Abstract

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It is known that the Toeplitz algebra associated with any flow which is both minimal and uniquely ergodic always has a trivial ${{K}_{1}}$-group. We show in this note that if the unique ergodicity is dropped, then such ${{K}_{1}}$-group can be non-trivial. Therefore, in the general setting of minimal flows, even the $K$-theoretical index is not sufficient for the classification of Toeplitz operators which are invertible modulo the commutator ideal.

Keywords

46L8047B3547C15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 2 , 01 June 1998 , pp. 240 - 244
Copyright
Copyright © Canadian Mathematical Society 1998

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