Shifted Substitution in Non-Commutative Multivariate Power Series with a View Toward Free Probability

被引：2

作者：

Ebrahimi-Fard, Kurusch ^{[1
]}

Patras, Frederic ^{[2
]}

Tapia, Nikolas ^{[3
,4
]}

Zambotti, Lorenzo ^{[5
]}

机构：

[1] Norwegian Univ Sci & Technol, Dept Math Sci, NO-7491 Trondheim, Norway

[2] Univ Cote dAzur, CNRS, UMR 7351, Parc Valrose, F-06108 Nice 02, France

[3] Weierstrass Inst Berlin, Berlin, Germany

[4] Tech Univ Berlin, Berlin, Germany

[5] Univ Paris Cite, Sorbonne Univ, LPSM, CNRS, 4 Pl Jussieu, F-75005 Paris, France

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2023年 / 19卷

基金：

欧洲研究理事会;

关键词：

non-commutative probability theory; non-commutative power series; moments and cumulants; combinatorial Hopf algebra; pre-Lie algebra; APPELL POLYNOMIALS; HOPF-ALGEBRAS; CUMULANTS; MONOTONE;

D O I：

10.3842/SIGMA.2023.038

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：17

共 26 条

[1] Appell polynomials and their relatives [J].