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 with a pre-Lie structure on formal power series. We study thes...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2023 |
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2023
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211905 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Shifted Substitution in Non-Commutative Multivariate Power Series with a View Toward Free Probability. Kurusch Ebrahimi-Fard, Frédéric Patras, Nikolas Tapia and Lorenzo Zambotti. SIGMA 19 (2023), 038, 17 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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 with 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.
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| ISSN: | 1815-0659 |