论文标题
通过标记的图组素的Ultragraph代数，应用于广义唯一定理
Ultragraph algebras via labelled graph groupoids, with applications to generalized uniqueness theorems
论文作者
论文摘要
Ultragraph产生具有某些特定属性的标记图。在本文中，我们描述了与标记的图形相关的代数等代数。更确切地说，我们表明，超级c* - 代数的已知群体素代数实现仅适用于每个边缘的范围是有限的超图，并且我们将此实现扩展到任何超图（包括带有水槽的超级）。使用我们的机械，我们将与超级相关的偏移空间表征为与Ultragraph相关的反向半群的紧密频谱（被视为标记的图）。此外，在纯粹的代数环境中，我们表明代数部分动作用来描述leavitt路径代数为部分偏斜群环，等同于拓扑部分动作的双重偏斜，我们使用此用来将其用于将Ultragraph Leavitt Leavitt path algebras描述为Steinberg Algebebras。最后，我们证明了Ultragraph C* - 代数和Ultragraph Leavitt Path代数的广义唯一定理，并表征其Abelian Core Subsalgebras。
An ultragraph gives rise to a labelled graph with some particular properties. In this paper we describe the algebras associated to such labelled graphs as groupoid algebras. More precisely, we show that the known groupoid algebra realization of ultragraph C*-algebras is only valid for ultragraphs for which the range of each edge is finite, and we extend this realization to any ultragraph (including ultragraphs with sinks). Using our machinery, we characterize the shift space associated to an ultragraph as the tight spectrum of the inverse semigroup associated to the ultragraph (viewed as a labelled graph). Furthermore, in the purely algebraic setting, we show that the algebraic partial action used to describe an ultragraph Leavitt path algebra as a partial skew group ring is equivalent to the dual of a topological partial action, and we use this to describe ultragraph Leavitt path algebras as Steinberg algebras. Finally, we prove generalized uniqueness theorems for both ultragraph C*-algebras and ultragraph Leavitt path algebras and characterize their abelian core subalgebras.
