Abstract

This letter is divided in two parts. In the first one it will be shown that the datum of a post-Lie product is equivalent to the one of an invertible crossed morphism between two Lie algebras. Moreover it will be argued that the integration of such a crossed morphism yields the post-Lie Magnus expansion associated to the original post-Lie algebra. The second part is devoted to present two combinatorial methods to compute the coefficients of this remarkable formal series. Both methods are based on special tubings on planar trees.

中文翻译：

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交叉态射，后李代数和后李马格努斯展开的整合

摘要

这封信分为两部分。在第一个中，将证明后李乘积的数据等价于两个李代数之间的可逆交叉态射之一。此外，有人会争辩说，这种交叉态射的积分产生了与原始后李代数相关的后李马格努斯展开。第二部分致力于提出两种组合方法来计算这个非凡的形式级数的系数。这两种方法都基于平面树上的特殊管道。