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NEST ALGEBRAS WITH LOCALLY CONSTANT COCYCLES

Published online by Cambridge University Press:  01 June 1997

ALLAN P. DONSIG  and
JUSTIN R. PETERS
ALLAN P. DONSIG
Affiliation:
Department of Mathematics, Lancaster University, Lancaster LA1 4YF
JUSTIN R. PETERS
Affiliation:
Department of Mathematics, Iowa State University, Ames, Iowa 50011. E-mail: [email protected]
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Abstract

The first examples of triangular AF algebras to be studied were the refinement algebra and the standard algebra. Both are analytic algebras with the property that the cocycle can be taken to be constant on the matrix units of the algebra. The latter property, called local constancy, is quite special and is still ill-understood. In the present paper we examine the class of nest algebras [Tscr ] in AF C*-algebras which share the distinctive features of the refinement algebra:

(1) [Tscr ] is a nest algebra in which the nest generates the diagonal,

(2) [Tscr ] admits a locally constant cocycle.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 55 , Issue 3 , June 1997 , pp. 569 - 587
Copyright
The London Mathematical Society 1997

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