论文标题
规律性结构中的Lie后代数
Post-Lie algebras in Regularity Structures
论文作者
论文摘要
在这项工作中，我们构建了从规律性结构理论理论作为后代代数的普遍包膜中构建了变形的屠夫 - 康涅斯kreimer hopf代数。我们表明，可以使用在奇异SPDE的背景下提出的两个组合结构中的任何一个：装饰的树木和多indices来完成。我们的构建灵感来自多个指数，在这些构建中，HOPF代数是作为Lie代数的通用信封，并且已经证明，人们可以找到与某些元素相称的基础。我们表明，这个谎言代数来自基本的lie后结构。
In this work, we construct the deformed Butcher-Connes-Kreimer Hopf algebra coming from the theory of Regularity Structures as the universal envelope of a post-Lie algebra. We show that this can be done using either of the two combinatorial structures that have been proposed in the context of singular SPDEs: decorated trees and multi-indices. Our construction is inspired from multi-indices where the Hopf algebra was obtained as the universal envelope of a Lie algebra and it has been proved that one can find a basis that is symmetric with respect to certain elements. We show that this Lie algebra comes from an underlying post-Lie structure.
