标题： $3$-dimensional Bol loops as sections in non-solvable Lie groups 显示英文标题

标题： $3$-dimensional Bol loops as sections in non-solvable Lie groups

摘要： 我们在这篇论文中的目标是分类具有非可解群作为其左平移在拓扑上生成的群的$3$维连通微分流形 Bol 乘法结构，并描述它们与度量空间几何的关系。 全局微分流形 Bol 乘法结构的分类与局部微分流形 Bol 乘法结构的分类有显著不同。 我们将可微的Bol环视为全局可微截面$\sigma :G/H \to G$的像，使得对于所有$r,s \in \sigma (G/H)$，元素$rsr$位于$\sigma (G/H)$中，其中$H$是单位元$e$在$L$中的稳定子群，在$G$中。 显示英文摘要

摘要： Our aim in this paper is to classify the $3$-dimensional connected differentiable global Bol loops, which have a non-solvable group as the group topologically generated by their left translations and to describe their relations to metric space geometries. The classification of global differentiable Bol loops significantly differs from the classification of local differentiable Bol loops. We treat the differentiable Bol loops as images of global differentiable sections $\sigma :G/H \to G$ such that for all $r,s \in \sigma (G/H)$ the element $rsr$ lies in $\sigma (G/H)$, where $H$ is the stabilizer of the identity $e$ of $L$ in $G$.