论文标题
转移的替换在非交通性多元电源系列中，并观察到自由概率
Shifted Substitution in Non-Commutative Multivariate Power Series with a View Toward Free Probability
论文作者
论文摘要
我们研究了一项针对正式功率序列的特定群体定律，该法在其解释为线性形式引起的非交通变量中，这是在适当的分级连接的单词Hopf代数上。该组定律是左线的，因此与正式力量序列的前lie结构有关。我们研究了这些结构，并展示了它们如何用于在群体理论中重铸，形成了正式功率序列的各种身份和变换，这些身份和转换在非交通概率理论的背景下，尤其是在Voiculescu的自由概率理论中。
We study a particular group law on formal power series in non-commuting variables induced by their interpretation as linear forms on a suitable graded connected word Hopf algebra. This group law is left-linear and is therefore associated to a pre-Lie structure on formal power series. We study these structures and show how they can be used to recast in a group theoretic form various identities and transformations on formal power series that have been central in the context of non-commutative probability theory, in particular in Voiculescu's theory of free probability.
