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Homology for operator algebras IV: n the regular classifications of limits of 4-cycle algebras.

Power, Stephen C. and Donsig, A. P. (1997) Homology for operator algebras IV: n the regular classifications of limits of 4-cycle algebras. Journal of Functional Analysis, 150 (1). pp. 240-287. ISSN 0022-1236

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Abstract

A 4-cycle algebra is a finite-dimensional digraph algebra (CSL algebra) whose reduced digraph is a 4-cycle. A rigid embedding between such algebras is a direct sum of certain nondegenerate multiplicity one star-extendible embeddings. A complete classification is obtained for the regular isomorphism classes of direct systemsAof 4-cycle algebras with rigid embeddings. The critical invariant is a binary relation inK0AH1A, generalising the scale of theK0group, called the joint scale. The joint scale encapsulates other invariants and compatibility conditions of regular isomorphism. These include the scale ofH1A, the scale ofH0AH1A, sign compatibility, congruence compatibility andH0H1coupling classes. These invariants are also important for liftingK0H1isomorphisms to algebra isomorphisms; we resolve this lifting problem for various classes of 4-cycle algebra direct systems

Item Type: Article
Journal or Publication Title: Journal of Functional Analysis
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 19507
Deposited By: ep_ss_importer
Deposited On: 11 Nov 2008 16:52
Refereed?: Yes
Published?: Published
Last Modified: 09 Oct 2013 13:12
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/19507

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