Lie's correspondence for commutative automorphic formal loops
Lie's correspondence for commutative automorphic formal loops
复制标题
可交换自守形式循环的李氏对应
DOI：
10.1016/j.laa.2018.01.028
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发表时间：
2016
影响因子：
1.1
通讯作者：
J. M. P'erez
中科院分区：
文献类型：
--
作者：
A. Grishkov;J. M. P'erez
我们建立了交换自同构形式环的Lie对应，它是非结合阿贝尔群的自然候选者，展示了基于Hopf代数的线性化技术如何应用于研究非线性结构。在特征为零的域上，证明了交换自同构形式环范畴等价于某个李三系范畴。借助于3×3矩阵的代数中系数的形式幂级数，还得到了这类回路的Baker-Campbell-Hausdorff公式。我们的公式与函数(e2 S−e2t)(S+t)2(e2(S+t)−1)密切相关。
We develop Lie's correspondence for commutative automorphic formal loops, which are natural candidates for non-associative abelian groups, to show how linearization techniques based on Hopf algebras can be applied to study non-linear structures. Over fields of characteristic zero, we prove that the category of commutative automorphic formal loops is equivalent to certain category of Lie triple systems. An explicit Baker–Campbell–Hausdorff formula for these loops is also obtained with the help of formal power series with coefficients in the algebra of 3 by 3 matrices. Our formula is strongly related to the function (e 2 s− e 2 t)(s+ t) 2 (e 2 (s+ t)− 1).