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

Research output: Contribution to journalJournal article

Published

Journal publication date15/10/1997
JournalJournal of Functional Analysis
Journal number1
Volume150
Number of pages48
Pages240-287
Original languageEnglish

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