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Approximately finitely acting operator algebras.

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Approximately finitely acting operator algebras. / Power, Stephen C.
In: Journal of Functional Analysis, Vol. 189, No. 2, 10.03.2002, p. 409-468.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Power, SC 2002, 'Approximately finitely acting operator algebras.', Journal of Functional Analysis, vol. 189, no. 2, pp. 409-468. https://doi.org/10.1006/jfan.2001.3858

APA

Power, S. C. (2002). Approximately finitely acting operator algebras. Journal of Functional Analysis, 189(2), 409-468. https://doi.org/10.1006/jfan.2001.3858

Vancouver

Power SC. Approximately finitely acting operator algebras. Journal of Functional Analysis. 2002 Mar 10;189(2):409-468. doi: 10.1006/jfan.2001.3858

Author

Power, Stephen C. / Approximately finitely acting operator algebras. In: Journal of Functional Analysis. 2002 ; Vol. 189, No. 2. pp. 409-468.

Bibtex

@article{898b8ae4774c41b8848cb718dec91ad9,
title = "Approximately finitely acting operator algebras.",
abstract = "Let E be an operator algebra on a Hilbert space with finite-dimensional C*-algebra C*(E). A classification is given of the locally finite algebras A0=[formula](Ak, φk) and the operator algebras A=[formula](Ak, φk) obtained as limits of direct sums of matrix algebras over E with respect to star-extendible homomorphisms. The invariants in the algebraic case consist of an additive semigroup, with scale, which is a right module for the semiring VE=Homu(E, E) of unitary equivalence classes of star-extendible homomorphisms. This semigroup is referred to as the dimension module invariant. In the operator algebra case the invariants consist of a metrized additive semigroup with scale and a contractive right module VE-action. Subcategories of algebras determined by restricted classes of embeddings, such as 1-decomposable embeddings between digraph algebras, are also classified in terms of simplified dimension modules.",
keywords = "operator algebra, approximately finite, nonselfadjoint, classification, metrized semiring",
author = "Power, {Stephen C.}",
note = "RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics",
year = "2002",
month = mar,
day = "10",
doi = "10.1006/jfan.2001.3858",
language = "English",
volume = "189",
pages = "409--468",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press Inc.",
number = "2",

}

RIS

TY - JOUR

T1 - Approximately finitely acting operator algebras.

AU - Power, Stephen C.

N1 - RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics

PY - 2002/3/10

Y1 - 2002/3/10

N2 - Let E be an operator algebra on a Hilbert space with finite-dimensional C*-algebra C*(E). A classification is given of the locally finite algebras A0=[formula](Ak, φk) and the operator algebras A=[formula](Ak, φk) obtained as limits of direct sums of matrix algebras over E with respect to star-extendible homomorphisms. The invariants in the algebraic case consist of an additive semigroup, with scale, which is a right module for the semiring VE=Homu(E, E) of unitary equivalence classes of star-extendible homomorphisms. This semigroup is referred to as the dimension module invariant. In the operator algebra case the invariants consist of a metrized additive semigroup with scale and a contractive right module VE-action. Subcategories of algebras determined by restricted classes of embeddings, such as 1-decomposable embeddings between digraph algebras, are also classified in terms of simplified dimension modules.

AB - Let E be an operator algebra on a Hilbert space with finite-dimensional C*-algebra C*(E). A classification is given of the locally finite algebras A0=[formula](Ak, φk) and the operator algebras A=[formula](Ak, φk) obtained as limits of direct sums of matrix algebras over E with respect to star-extendible homomorphisms. The invariants in the algebraic case consist of an additive semigroup, with scale, which is a right module for the semiring VE=Homu(E, E) of unitary equivalence classes of star-extendible homomorphisms. This semigroup is referred to as the dimension module invariant. In the operator algebra case the invariants consist of a metrized additive semigroup with scale and a contractive right module VE-action. Subcategories of algebras determined by restricted classes of embeddings, such as 1-decomposable embeddings between digraph algebras, are also classified in terms of simplified dimension modules.

KW - operator algebra

KW - approximately finite

KW - nonselfadjoint

KW - classification

KW - metrized semiring

U2 - 10.1006/jfan.2001.3858

DO - 10.1006/jfan.2001.3858

M3 - Journal article

VL - 189

SP - 409

EP - 468

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 2

ER -