Approximately finitely acting operator algebras
| dc.creator | Power, S. C. | |
| dc.date | 2000-05-11 | |
| dc.date.accessioned | 2026-07-07T04:35:11Z | |
| dc.date.available | 2026-07-07T04:35:11Z | |
| dc.description | Let E be an operator algebra on a Hilbert space with finite-dimensional generated C*-algebra. A classification is given of the locally finite algebras and the operator algebras 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 $V_E = Hom_u(E \otimes \sK, E \otimes \sK)$ 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 $V_E$-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 module invariants. | |
| dc.description | 65 pages | |
| dc.identifier | https://arxiv.org/abs/math/0005110 | |
| dc.identifier | http://arxiv.org/abs/math/0005110 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59172 | |
| dc.subject | Operator Algebras | |
| dc.subject | 47L40 | |
| dc.title | Approximately finitely acting operator algebras | |
| dc.type | text |