Enveloping Algebras of Prelie Algebras, Solomon idempotents and the Magnus Formula
Enveloping Algebras of Prelie Algebras, Solomon idempotents and the Magnus Formula
复制标题
Prelie 代数的包络代数、所罗门幂等和马格努斯公式
DOI：
10.1142/s0218196713400134
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
F. Patras
中科院分区：
文献类型：
--
作者：
F. Chapoton;F. Patras
研究了preLie代数的包络代数的内部结构。我们特别表明，所产生的庞加莱-伯克霍夫-维特定理的典型的投影可以明确计算。它们恰好与矩阵微分方程的马格努斯公式密切相关。事实上，我们表明，马格努斯公式提供了一种方法来计算preLie代数上的规范投影。相反，我们的研究结果提供了新的见解经典问题的微分方程理论和最近的进展，他们的组合理解。
We study the internal structure of enveloping algebras of preLie algebras. We show in particular that the canonical projections arising from the Poincare–Birkhoff–Witt theorem can be computed explicitly. They happen to be closely related to the Magnus formula for matrix differential equations. Indeed, we show that the Magnus formula provides a way to compute the canonical projection on the preLie algebra. Conversely, our results provide new insights on classical problems in the theory of differential equations and on recent advances in their combinatorial understanding.