论文标题
分组不变的随机订单的扩展
Extensions of invariant random orders on groups
论文作者
论文摘要
在本文中，我们研究了一个可数组$γ$对集团订单空间的作用。特别是，我们关注该空间上不变的概率度量，称为不变的随机顺序。我们表明，对于任何可数组，随机不变订单的空间足够丰富，可以包含任何自由阵尾动作的同构副本，并表征可实现的非自由动作。我们证明了关于不变随机订单的单纯形的Glasner-Weiss二分法。我们还表明，$ \ mathrm {sl} _3（\ Mathbf {z}）上的零件订单与正向矩阵的半群相关的$不能扩展到不变的随机总订单。因此，我们为无法随机扩展的部分顺序（确定性或随机）提供了第一个示例。
In this paper we study the action of a countable group $Γ$ on the space of orders on the group. In particular, we are concerned with the invariant probability measures on this space, known as invariant random orders. We show that for any countable group the space of random invariant orders is rich enough to contain an isomorphic copy of any free ergodic action, and characterize the non-free actions realizable. We prove a Glasner-Weiss dichotomy regarding the simplex of invariant random orders. We also show that the invariant partial order on $\mathrm{SL}_3(\mathbf{Z})$ corresponding to the semigroup of positive matrices cannot be extended to an invariant random total order. We thus provide the first example for a partial order (deterministic or random) that cannot be randomly extended.
