Loading…

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

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...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2023-06
Main Authors: Ebrahimi-Fard, Kurusch, Patras, Frédéric, Tapia, Nikolas, Zambotti, Lorenzo
Format: Article
Language:English
Subjects:
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2204.01445