Home > Research > Publications & Outputs > Homology for operator algebras IV: n the regula...
View graph of relations

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

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Published

Standard

Homology for operator algebras IV: n the regular classifications of limits of 4-cycle algebras. / Power, Stephen C.; Donsig, A. P.
In: Journal of Functional Analysis, Vol. 150, No. 1, 15.10.1997, p. 240-287.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Harvard

APA

Vancouver

Power SC, Donsig AP. Homology for operator algebras IV: n the regular classifications of limits of 4-cycle algebras. Journal of Functional Analysis. 1997 Oct 15;150(1):240-287. doi: 10.1006/jfan.1997.3118

Author

Power, Stephen C. ; Donsig, A. P. / Homology for operator algebras IV: n the regular classifications of limits of 4-cycle algebras. In: Journal of Functional Analysis. 1997 ; Vol. 150, No. 1. pp. 240-287.

Bibtex

@article{975922efe1ac485d81e90287bbeb05d7,
title = "Homology for operator algebras IV: n the regular classifications of limits of 4-cycle algebras.",
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",
author = "Power, {Stephen C.} and Donsig, {A. P.}",
year = "1997",
month = oct,
day = "15",
doi = "10.1006/jfan.1997.3118",
language = "English",
volume = "150",
pages = "240--287",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press Inc.",
number = "1",

}

RIS

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 -