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Finite Lattices of Projections in Factors and Approximately Finite C*-Algebras

Published online by Cambridge University Press:  20 November 2018

S. C. Power
S. C. Power*
Affiliation:
Department of Mathematics Lancaster University Lancaster LA14YF England
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Abstract

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A unique factorisation theorem is obtained for tensor products of finite lattices of commuting projections in a factor. This leads to unique tensor product factorisations for reflexive subalgebras of the hyperfinite II1 factor which have irreducible finite commutative invariant projection lattices. It is shown that the finite refinement property fails for simple approximately finite C*-algebras, and this implies that there is no analogous general result for finite lattice subalgebras in this context.

Keywords

47D2546L05.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 1 , 01 March 1992 , pp. 116 - 125
Copyright
Copyright © Canadian Mathematical Society 1992

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