Analytic Taf Algebras

Peters, J. R. ; Poon, Y. T. ; Wagner, B. H.

Canadian journal of mathematics, Tome 45 (1993) no. 5, pp. 1009-1031

Résumé

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

Détail

DOI : 10.4153/CJM-1993-056-0

Mots-clés : 46H20, 46L05

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