论文标题
de Finetti-Type定理在准局部代数和无限费米张量产品上
de Finetti-type theorems on quasi-local algebras and infinite Fermi tensor products
论文作者
论文摘要
$ \ mathbb {p} _ \ mathbb {n} $的本地操作，$ \ mathbb {n} $上的有限排列，quasi-local代数上的定义并证明为$ \ \ mathbb {p} _ \ mathbb {p} _ \ mathbb {n n} $ - abelian。事实证明，当地行动下的不变状态甚至是自动的，极端不变的状态在强烈的聚集中。不变状态的尾部代数符合hewitt和野蛮定理的形式，因为它们与固定点的von Neumann代数相吻合。 $ C^*$ - 代数（包括汽车代数）的无限分级张量产品随后被称为$ \ Mathbb {p} _ \ Mathbb {n} $的特定示例。极端不变状态的特征是单个偶数状态的无限产物，并建立了de finetti定理。最后，通过应用扭曲的张量式换向定理的扭曲版本，这也是阶乘的无限产品。
Local actions of $\mathbb{P}_\mathbb{N}$, the group of finite permutations on $\mathbb{N}$, on quasi-local algebras are defined and proved to be $\mathbb{P}_\mathbb{N}$-abelian. It turns out that invariant states under local actions are automatically even, and extreme invariant states are strongly clustering. Tail algebras of invariant states are shown to obey a form of the Hewitt and Savage theorem, in that they coincide with the fixed-point von Neumann algebra. Infinite graded tensor products of $C^*$-algebras, which include the CAR algebra, are then addressed as particular examples of quasi-local algebras acted upon $\mathbb{P}_\mathbb{N}$ in a natural way. Extreme invariant states are characterized as infinite products of a single even state, and a de Finetti theorem is established. Finally, infinite products of factorial even states are shown to be factorial by applying a twisted version of the tensor product commutation theorem, which is also derived here.
