论文标题
部分可观测时空混沌系统的无模型预测
The planar $3$-colorable subgroup $\mathcal{E}$ of Thompson's group $F$ and its even part
论文作者
论文摘要
我们研究了汤普森（Thompson）的$ f $的平面$ 3 $ -Colorable子组$ \ MATHCAL {E} $，甚至其部分$ \ Mathcal {e} _ {\ rm eveven} $。后者是通过将$ \ Mathcal {e} $切成$ f $ isomorphic的有限索引子组的$ \ Mathcal {e} $获得的，即矩形子组$ k _ {（2,2）} $。我们表明，平面$ 3 $ 3 $ - 可油的子群的均匀部分$ \ Mathcal {e} _ {\ rm evev} $在适当的二元理性子集的稳定器方面接受了描述。结果，$ \ Mathcal {e} _ {\ rm even} $是从Golan和Sapir的意义上关闭的。然后，我们研究了与$ \ Mathcal {e} _ {\ rm evev} $相关的三个准常规表示：两个表明两个是不可约的，一个是可还原的。
We study the planar $3$-colorable subgroup $\mathcal{E}$ of Thompson's group $F$ and its even part $\mathcal{E}_{\rm EVEN}$. The latter is obtained by cutting $\mathcal{E}$ with a finite index subgroup of $F$ isomorphic to $F$, namely the rectangular subgroup $K_{(2,2)}$. We show that the even part $\mathcal{E}_{\rm EVEN}$ of the planar $3$-colorable subgroup admits a description in terms of stabilisers of suitable subsets of dyadic rationals. As a consequence $\mathcal{E}_{\rm EVEN}$ is closed in the sense of Golan and Sapir. We then study three quasi-regular representations associated with $\mathcal{E}_{\rm EVEN}$: two are shown to be irreducible and one to be reducible.
