论文标题
$ \ MATHCAL {C}^r $ -Differentia-loops的切线延长
Tangent prolongation of $\mathcal{C}^r$-differentiable loops
论文作者
论文摘要
我们论文的目的是将谎言基团的切线延长推广到非缔合性乘法，并检查如何将弱的关联和弱逆性质转移到切线束上定义的乘法中。我们得到$ \ Mathcal {C}^r $ -Differentiable Loop（$ r \ geq 1 $）的切线延长是$ \ MATHCAL {C}^{r-1} $ - 可获得的较小的弱和弱属性和弱的初始路线的弱属性和弱的属性。
The aim of our paper is to generalize the tangent prolongation of Lie groups to non-associative multiplications and to examine how the weak associative and weak inverse properties are transferred to the multiplication defined on the tangent bundle. We obtain that the tangent prolongation of a $\mathcal{C}^r$-differentiable loop ($r\geq 1$) is a $\mathcal{C}^{r-1}$-differentiable loop that acquires the classical weak inverse and weak associative properties of the initial loop.
