1 1 M ay 2 00 0 APPROXIMATELY FINITELY ACTING OPERATOR ALGEBRAS
نویسنده
چکیده
−→ (Ak, φk) and the operator algebras A = lim −→ (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⊗K, E⊗K) 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.
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