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1 results

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

  • Terry A. Loring
  • Journal:
    Canadian Journal of Mathematics / Volume 43 / Issue 1 / 01 February 1991
    Published online by Cambridge University Press:
    20 November 2018, pp. 119-157
    Print publication:
    01 February 1991
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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.