On the solutions of universal differential equation by noncommutative Picard-Vessiot theory
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866917158292815872 |
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| author | Bui, V. C. Minh, V. Hoang Ngoc Dinh, V. Nguyen Ngo, Q. H. |
| author_facet | Bui, V. C. Minh, V. Hoang Ngoc Dinh, V. Nguyen Ngo, Q. H. |
| contents | Basing on Picard-Vessiot theory of noncommutative differential equations and algebraic combinatorics on noncommutative formal series with holomorphic coefficients, various recursive constructions of sequences of grouplike series converging to solutions of universal differential equation are proposed. Basing on monoidal factorizations, these constructions intensively use diagonal series and various pairs of bases in duality, in concatenation-shuffle bialgebra and in a Loday's generalized bialgebra. As applications, the unique solution, satisfying asymptotic conditions, of Knizhnik-Zamolodchikov equations is provided by dévissage. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2209_08596 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the solutions of universal differential equation by noncommutative Picard-Vessiot theory Bui, V. C. Minh, V. Hoang Ngoc Dinh, V. Nguyen Ngo, Q. H. Mathematical Physics Basing on Picard-Vessiot theory of noncommutative differential equations and algebraic combinatorics on noncommutative formal series with holomorphic coefficients, various recursive constructions of sequences of grouplike series converging to solutions of universal differential equation are proposed. Basing on monoidal factorizations, these constructions intensively use diagonal series and various pairs of bases in duality, in concatenation-shuffle bialgebra and in a Loday's generalized bialgebra. As applications, the unique solution, satisfying asymptotic conditions, of Knizhnik-Zamolodchikov equations is provided by dévissage. |
| title | On the solutions of universal differential equation by noncommutative Picard-Vessiot theory |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2209.08596 |