Shifted substitution in non-commutative multivariate power series with a view toward free probability - Archive ouverte HAL
Article Dans Une Revue Symmetry, Integrability and Geometry : Methods and Applications Année : 2023

Shifted substitution in non-commutative multivariate power series with a view toward free probability

Résumé

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.

Dates et versions

hal-03806591 , version 1 (07-10-2022)

Identifiants

Citer

Kurusch Ebrahimi-Fard, Frédéric Patras, Nikolas Tapia, Lorenzo Zambotti. Shifted substitution in non-commutative multivariate power series with a view toward free probability. Symmetry, Integrability and Geometry : Methods and Applications, 2023, ⟨10.3842/SIGMA.2023.038⟩. ⟨hal-03806591⟩
20 Consultations
0 Téléchargements

Altmetric

Partager

More