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Algebraic orders and chordal limit algebras

Published online by Cambridge University Press:  20 January 2009

Allan P. Donsig
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Abstract

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We develop an isomorphism invariant for limit algebras: an extension of Power's strong algebraic order on the scale of the K0-group (Power, J. Operator Theory 27 (1992), 87–106). This invariant is complete for a certain family of limit algebras: inductive limits of digraph algebras (a.k.a. finite dimensional CSL algebras) satisfying two conditions: (1) the inclusions of the digraph algebras respect the order-preserving normalisers, and (2) the digraph algebras have chordal digraphs. The first condition is also used to show that the invariant depends only on the limit algebra and not the direct system. We give an intrinsic characterisation of the limit algebra and not the direct system. We give an intrinsic characterisation of the limit algebras satisfying both (1) and (2).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 41 , Issue 3 , October 1998 , pp. 465 - 485
Copyright
Copyright © Edinburgh Mathematical Society 1998

Footnotes

*

Partially supported by an NSERC of Canada Postdoctoral Fellowship.

Current Address: Department of Mathematics & Statistics, University of Nebraska-Lincoln, Lincoln, NE, U.S.A. 68588–0323 E-mail: [email protected]

References

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