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Approximately finitely acting operator algebras.

Research output: Contribution to journalJournal article

Published

Journal publication date10/03/2002
JournalJournal of Functional Analysis
Journal number2
Volume189
Number of pages60
Pages409-468
Original languageEnglish

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.

Bibliographic note

RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics