标题： 德·菲内蒂定理在无限非交换环面 显示英文标题

标题： De Finetti Theorem on the infinite non-commutative torus

摘要： 在无限非交换环面上的可扩展态集\mathbb{A}_{\mathbb{Z}_\alpha }对所有形变参数{\alpha }的值都已确定。如果{\alpha }是无理数，那么规范迹是唯一的可扩展 2{\pi }态。如果{\alpha }是有理数，所有可扩展态的集合是一个 Bauer 2{\pi }单纯形。此外，其边界是 C(T) 上单个态的无限乘积的集合。 最后，所有在\mathbb{A}_{\mathbb{Z}_\alpha }上的平稳状态的单纯形被证明是Poulsen单纯形，对于变形参数{\alpha }的所有值都是如此。 显示英文摘要

摘要： The set of spreadabl estates on an infinite non-commutive torus \mathbb{A}_{\mathbb{Z}_\alpha} is determined for all values of the deformation parameter {\alpha}. If {\alpha} is irrational, the canonical trace is the only spreadable 2{\pi} state. If {\alpha} is rational, the set of all spreadable states is a Bauer 2{\pi} simplex. Moreover, its boundary is the set of all infinite products of a single state on C(T). Finally, the simplex of all stationary states on \mathbb{A}_{\mathbb{Z}_\alpha} is proved to be the Poulsen simplex for all values of the deformation parameter {\alpha}.