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arXiv · 2402.16450

A post-group theoretic perspective on the operator-valued S-transform in free probability

Kurusch Ebrahimi-Fard·Timothé Ringeard
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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.

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Kurusch Ebrahimi-Fard, Timothé Ringeard. 2024-02-26. A post-group theoretic perspective on the operator-valued S-transform in free probability. https://arxiv.org/abs/2402.16450

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