论文标题
拓扑图的重建及其希尔伯特双模型
Reconstruction of topological graphs and their Hilbert bimodules
论文作者
论文摘要
我们表明，与紧凑型拓扑图相关的希尔伯特双模模可以从图形的toeplitz代数，其规格作用和函数的交换子代理中的c* - 代数三重三倍中恢复。我们讨论了与戴维森·卡索斯（Davidson-Katsoulis）和戴维森·罗伊多（Davidson-Roydor）的作品有关拓扑图的本地结合和张量代数的同构的联系。特别是，我们提供了一个直接证明，即可以从其希尔伯特·比米模型中恢复紧凑的拓扑图，以恢复局部轭，并提供了非同构的局部共轭紧凑型拓扑图的示例，该示例与同构Hilbert bimodules。我们还提供了一个基本的证据，表明对于具有完全断开的顶点空间的紧凑型拓扑图，局部结合性，希尔伯特·比模构的概念，c* - 代数三倍的同构，同构和同构的同构和同构。
We show that the Hilbert bimodule associated to a compact topological graph can be recovered from the C*-algebraic triple consisting of the Toeplitz algebra of the graph, its gauge action and the commutative subalgebra of functions on the vertex space of the graph. We discuss connections with work of Davidson-Katsoulis and of Davidson-Roydor on local conjugacy of topological graphs and isomorphism of their tensor algebras. In particular, we give a direct proof that a compact topological graph can be recovered up to local conjugacy from its Hilbert bimodule, present an example of nonisomorphic locally conjugate compact topological graphs with isomorphic Hilbert bimodules. We also give an elementary proof that for compact topological graphs with totally disconnected vertex space the notions of local conjugacy, Hilbert bimodule isomorphism, isomorphism of C*-algebraic triples, and isomorphism all coincide.
