A post-group theoretic perspective on the operator-valued S-transform in free probability
Operator Algebras
2024-02-27 v1 Group Theory
Abstract
We investigate the algebraic structure underlying Voiculescu's S-transform in the setting of operator-valued free probability. We show that its twisted factorisation property gives rise to post-groups, crossed morphisms, as well as pre- and post-Lie algebras.
Keywords
Cite
@article{arxiv.2402.16450,
title = {A post-group theoretic perspective on the operator-valued S-transform in free probability},
author = {Kurusch Ebrahimi-Fard and Timothé Ringeard},
journal= {arXiv preprint arXiv:2402.16450},
year = {2024}
}