$C^{*}$ -模的有限逼近性质
Finite approximation properties of $C^{*}$-modules
摘要：
研究了$C^{*}$ -代数上的模映射的核性和正合性的概念，这些模映射是另一个具有相容作用的$C^*$ -代数上的$C^*$ -模，并考察了这些$C^*$ -模的有限逼近性质.我们证明模块版本的Kirchberg和Choi-Effros的结果。作为一个具体的例子，我们将可数离散群上的约化$C^*$ -代数和von Neumann代数的有限维逼近性质推广到可数逆半群上的这些算子代数，这些算子代数的模结构来自于$C^*$ -代数在幂等子半群上的作用.
英文摘要：
We study the notions of nuclearity and exactness for module maps on $C^{*}$-algebras which are $C^*$-module over another $C^*$-algebra with compatible actions and examine finite approximation properties of such $C^*$-modules. We prove module versions of the results of Kirchberg and Choi-Effros. As a concrete example we extend the finite dimensional approximation properties of reduced $C^*$-algebras and von Neumann algebras on countable discrete groups to these operator algebras on countable inverse semigroups with the module structure coming from the action of the $C^*$-algebras on the subsemigroup of idempotents.
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