论文标题
与图形和类别相关的操作员代数：调查
Operator algebras associated with graphs and categories of paths: a Survey
论文作者
论文摘要
可以通过有向图构建许多有趣代数的有趣示例，无论是自我拥护者还是非自我辅助的示例。在这项调查中，我们概述了来自定向图的$ C^*$ - 代数的构建，以及两个图形的概括：高级图和路径类别。我们还研究了从图和较高级别图产生的自由半摩群代数，重点是左规则的自由半摩群代数。我们提供了特定图和它们产生的代数的示例，并讨论了诸如半透明性和反思性等属性。最后，我们提出了一种新的结构：将左侧的常规免费半摩型结构应用于路径类别。
Many interesting examples of operator algebras, both self-adjoint and non-self-adjoint, can be constructed from directed graphs. In this survey, we overview the construction of $C^*$-algebras from directed graphs and from two generalizations of graphs: higher rank graphs and categories of paths. We also look at free semigroupoid algebras generated from graphs and higher rank graphs, with an emphasis on the left regular free semigroupoid algebra. We give examples of specific graphs and the algebras they generate, and we discuss properties such as semisimplicity and reflexivity. Finally, we propose a new construction: applying the left regular free semigroupoid construction to categories of paths.
