论文标题
部分可观测时空混沌系统的无模型预测
Forest-skein groups II: construction from homogeneously presented monoids
论文作者
论文摘要
受沃恩·琼斯（Vaughan Jones）的共同田野理论的重建计划的启发，我们最近引入了一类称为“森林 - 斯凯恩（Forest-Skein offer）”集团。它们是根据绞线演示文稿建造的：一组颜色和一对彩色树。每个漂亮的绞线演示文稿都会产生与理查德·汤普森（Richard Thompson）的F，T，V和Brin和DeHornoy的编织版本类似的四个组。 在本文中，我们考虑了从一维绞线演示文稿获得的森林 - 金族群体；同质单体呈现的数据。我们将这些群体分解为花圈产品。这允许将它们分类为同构。此外，我们证明，单粒细分组的许多特性都通过了森林 - 金蛋白群，例如Haagerup属性，同源和拓扑有限属性以及有序性。
Inspired by the reconstruction program of conformal field theories of Vaughan Jones we recently introduced a vast class of so called forest-skein groups. They are built from a skein presentation: a set of colours and a set of pairs of coloured trees. Each nice skein presentation produces four groups similar to Richard Thompson's group F,T,V and the braided version BV of Brin and Dehornoy. In this article, we consider forest-skein groups obtained from one-dimensional skein presentations; the data of a homogeneous monoid presentation. We decompose these groups as wreath products. This permits to classify them up to isomorphisms. Moreover, we prove that a number of properties of the fraction group of the monoid pass through the forest-skein groups such as the Haagerup property, homological and topological finiteness properties, and orderability.
