| Autor: |
Ebrahimi-Fard, Kurusch, Patras, Frédéric, Tapia, Nikolas, Zambotti, Lorenzo |
| Rok vydání: |
2022 |
| Předmět: |
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| Zdroj: |
SIGMA 19 (2023), 038, 17 pages |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.3842/SIGMA.2023.038 |
| Popis: |
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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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