Post-Hopf algebra in non-commutative probability theory
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913589387853824 |
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| author | Gilliers, Nicolas |
| author_facet | Gilliers, Nicolas |
| contents | We study $\mathcal{O}$-operators and post-Lie products over the same Lie algebra compatible in a certain sense. We prove that the group product corresponding to the formal integration of the Lie algebra, which is adjacent to the sum of two compatible post-Lie products, can be factorized in a way reminiscent of the classical Semenov-Tian-Shanskii factorization. In the second part, we explore applications in non-commutative probability. We introduce new transforms that facilitate the computation of conditionally free and conditionally monotone multiplicative convolutions involving operator-valued non-commutative distributions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02670 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Post-Hopf algebra in non-commutative probability theory Gilliers, Nicolas Operator Algebras Rings and Algebras 17B60, 46L53 We study $\mathcal{O}$-operators and post-Lie products over the same Lie algebra compatible in a certain sense. We prove that the group product corresponding to the formal integration of the Lie algebra, which is adjacent to the sum of two compatible post-Lie products, can be factorized in a way reminiscent of the classical Semenov-Tian-Shanskii factorization. In the second part, we explore applications in non-commutative probability. We introduce new transforms that facilitate the computation of conditionally free and conditionally monotone multiplicative convolutions involving operator-valued non-commutative distributions. |
| title | Post-Hopf algebra in non-commutative probability theory |
| topic | Operator Algebras Rings and Algebras 17B60, 46L53 |
| url | https://arxiv.org/abs/2404.02670 |