近似双作用算子代数
Approximately finitely acting operator algebras
摘要：
设E是希尔伯特空间上的一个算子代数，其生成C* 代数是有限维的.本文给出了局部有限代数的一个分类，并给出了作为E上矩阵代数关于星可扩同态的直和的极限而得到的算子代数的分类。代数情形下的不变量由一个带标度的加法半群组成，它是星可扩同态的酉等价类的半环$V_E = Hom_u(E \otimes \sK, E \otimes \sK)$的右模。这个半群称为维数模不变量。在算子代数情形下，不变量由一个带标度的度量化加法半群和一个压缩右模$V_E$ -作用组成。由有限嵌入类确定的代数的子范畴，如有向图代数之间的1-可分解嵌入，也可以根据简化的维数模不变量进行分类。
英文摘要：
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.
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