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Journal of the London Mathematical Society 1997 55(3):569-587; doi:10.1112/S0024610797005127
© 1997 by London Mathematical Society
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© The London Mathematical Society

Nest Algebras with Locally Constant Cocycles

Allan P. Donsig and Justin R. Peters

Department of Mathematics, Lancaster University Lancaster LA1 4YF
Department of Mathematics, Iowa State University Ames, Iowa 50011 USA. E-mail: peters{at}iastate.edu

Received 10 October 1994. Revision received 9 May 1995.

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 T in AF C*-algebras which share the distinctive features of the refinement algebra:

(1) T is a nest algebra in which the nest generates the diagonal,

(2) T admits a locally constant cocycle.

Department of Pure Mathematics University of Waterloo Waterloo Ontario Canada N2L 361 E-mail: apdonsig{at}math.uwaterloo.ca


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