Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Homology for operator algebras IV: n the regular classifications of limits of 4-cycle algebras.
AU - Power, Stephen C.
AU - Donsig, A. P.
PY - 1997/10/15
Y1 - 1997/10/15
N2 - 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
AB - 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
U2 - 10.1006/jfan.1997.3118
DO - 10.1006/jfan.1997.3118
M3 - Journal article
VL - 150
SP - 240
EP - 287
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 1
ER -