Research output: Contribution to journal › Journal article

Published

<mark>Journal publication date</mark> | 10/03/2002 |
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<mark>Journal</mark> | Journal of Functional Analysis |

Issue number | 2 |

Volume | 189 |

Number of pages | 60 |

Pages (from-to) | 409-468 |

<mark>State</mark> | Published |

<mark>Original language</mark> | English |

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.

RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics