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Berg's Technique for Pseudo-Actions With Applications to af Embeddings

Published online by Cambridge University Press:  20 November 2018

Terry A. Loring
Terry A. Loring*
Affiliation:
Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, Nova Scotia B3H 3J5
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Abstract

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Berg's interchange technique is generalized to the context of certain new objects called pseudo-actions. This is used to find a more geometric proof of the Pimsner-Voiculescu theorem on the AF embedding of the irrational rotation algebras. Connections with Berg's original results are briefly examined.

Embedding diagrams are introduced to provide a uniform way of describing embeddings of transformation group C*-algebras C(X) ⋊ ℤ into AF algebras. Pimsner has classified the transformation group C* -algebras which can be AF embedded. We present a new proof of this result using embedding diagrams and pseudo-actions. The need to calculate the join of an open cover with its iterates under the transformation has been eliminated.

Keywords

46L0547A5554H20Berg's techniqueAF algebraAF embeddingtransformation group C*-algebra
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 1 , 01 February 1991 , pp. 119 - 157
Copyright
Copyright © Canadian Mathematical Society 1991

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