论文标题
离散量子结构
Discrete quantum structures
论文作者
论文摘要
大多数已建立的离散结构的量子泛化被证明是单个量子泛化的实例。特别是，杜安，塞维利尼和冬季的量子图，库珀贝格和韦弗的量子公制空间，atserias，mančinska，roberson，šámal，šámal，severini，severini和varvitsiotis的量子同构，以及在woronowicz的量子中，这些人都散发出了伊斯兰（Neys and and）。是一类离散量子结构的子类。这种离散的量子结构被定义为具有各种ARIT的关系和功能的离散量子空间。 Weaver的量子谓词逻辑是Birkhoff和Von Neumann的量子命题逻辑的概括，为大类特性提供了规范的量子概括。此处介绍的离散量子空间的平等关系在这种数学量化方法中起着核心作用。
A majority of established quantum generalizations of discrete structures are shown to be instances of a single quantum generalization. In particular, the quantum graphs of Duan, Severini and Winter, the quantum metric spaces of Kuperberg and Weaver, the quantum isomorphisms of Atserias, Mančinska, Roberson, Šámal, Severini and Varvitsiotis and the quantum groups of Woronowicz that are all discrete in the sense that the underlying von Neumann algebra is hereditarily atomic are shown to be subclasses of a single class of discrete quantum structures. Such a discrete quantum structure is defined to be a discrete quantum space equipped with relations and functions of various arities. Weaver's quantum predicate logic, a generalization of the quantum propositional logic of Birkhoff and von Neumann, provides canonical quantum generalizations for a large class of properties. The equality relation on discrete quantum spaces that is introduced here plays a central role in this approach to mathematical quantization.
