论文标题
$ \ mathbb {n} $ - 图$ c^*$ - 代数
$\mathbb{N}$-Graph $C^*$-Algebras
论文作者
论文摘要
在本文中，我们将$ k $ graph的概念概括为（可数）无限等级。然后，我们以与$ k $ -graph $ c^*$ - 代数相似的方式定义$ c^*$ - 代数。通过这种结构，我们能够找到对规格不变唯一性和cuntz-krieger唯一定理的类似物。我们还表明，$ \ mathbb {n} $ - 图$ c^*$ - 代数可以看作是$ k $ -graph $ c^*$ - 代数的电感限制。这提供了描述规格不变理想结构的好方法。此外，我们描述了我们$ n $ -graph $ c^*$ - 代数的常规规格不变理想的顶点集。然后，我们将$ \ mathbb {n} $的构造构建到代数设置中，并获得与$ C^*$ - 代数构建的许多相似之处。
In this paper we generalize the notion of a $k$-graph into (countable) infinite rank. We then define our $C^*$-algebra in a similar way as in $k$-graph $C^*$-algebras. With this construction we are able to find analogues to the Gauge Invariant Uniqueness and Cuntz-Krieger Uniqueness Theorems. We also show that the $\mathbb{N}$-graph $C^*$-algebras can be viewed as the inductive limit of $k$-graph $C^*$-algebras. This gives a nice way to describe the gauge-invariant ideal structure. Additionally, we describe the vertex-set for regular gauge-invariant ideals of our $N$-graph $C^*$-algebras. We then take our construction of the $\mathbb{N}$-graph into the algebraic setting and receive many similarities to the $C^*$-algebra construction.
