C* 矩阵的戈尔迪维度

Pub Date : 2024-01-11 DOI:10.1017/s0013091523000767
Mohammad Rouzbehani, Massoud Amini, Mohammad B. Asadi
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引用次数: 0

摘要

本文将介绍并研究 C* 代数的戈尔迪维度概念。我们证明,当且仅当一个 C* 代数的局部乘子代数的中心维数为 n 时,A 才具有戈尔迪维数 n。在这种情况下,A 具有有限维中心,其原始谱是极端断开的。此外,如果 A 是扩展的,我们会证明它分解为 n 个质数 C*-代数的直接和。特别是,每一个具有戈尔迪维度的稳定有限精确 C* 代数,如果具有投影性质和严格满元素,都会有一个满投影和一个非零的密集定义的下半连续迹。最后,我们证明某些具有戈尔迪维度的 C* 代数(不一定是简单的、可分离的或核的)是可以通过埃利奥特不变量来分类的。
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Goldie dimension for C*-algebras

In this article, we introduce and study the notion of Goldie dimension for C*-algebras. We prove that a C*-algebra A has Goldie dimension n if and only if the dimension of the center of its local multiplier algebra is n. In this case, A has finite-dimensional center and its primitive spectrum is extremally disconnected. If moreover, A is extending, we show that it decomposes into a direct sum of n prime C*-algebras. In particular, every stably finite, exact C*-algebra with Goldie dimension, that has the projection property and a strictly full element, admits a full projection and a non-zero densely defined lower semi-continuous trace. Finally we show that certain C*-algebras with Goldie dimension (not necessarily simple, separable or nuclear) are classifiable by the Elliott invariant.

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