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Analytic Taf Algebras

Published online by Cambridge University Press:  20 November 2018

J. R. Peters ,
Y. T. Poon  and
B. H. Wagner
J. R. Peters
Affiliation:
Department of Mathematics Iowa State University Ames, Iowa 50011 U.S.A.
Y. T. Poon
Affiliation:
Department of Mathematics Iowa State University Ames, Iowa 50011 U.S.A.
B. H. Wagner
Affiliation:
Department of Mathematics Iowa State University Ames, Iowa 50011 U.S.A.
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Abstract

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A strongly maximal triangular AF algebra which is defined by a realvalued cocycle is said to be analytic. Formulas for generic cocycles are given separately for both the integer-valued case and the real-valued coboundary case, and also for certain nest algebras. In the case of an integer-valued cocycle, there is an associated partial homeomorphismof the maximal ideal space of the diagonal. If the partial homeomorphism extends to a homeomorphism, then the algebra embeds in a crossed product. This occurs for a large class of subalgebras of UHF algebras, but an example shows that this does not always occur. An example is given of a triangular AF algebra which is analytic via a coboundary but is not a nest algebra; also, it is shown that a nest algebra need not be analytic

Keywords

46H2046L05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 5 , 01 October 1993 , pp. 1009 - 1031
Copyright
Copyright © Canadian Mathematical Society 1993

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