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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| Accès en ligne: | https://arxiv.org/abs/2312.16674 |
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| _version_ | 1866912038647758848 |
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| author | Ebrahimi-Fard, Kurusch Mencattini, Igor Quesney, Alexandre |
| author_facet | Ebrahimi-Fard, Kurusch Mencattini, Igor Quesney, Alexandre |
| contents | The Magnus expansion, introduced by Wilhelm Magnus in 1954, is an infinite Lie series employed to express solutions for first-order homogeneous linear differential equations involving a linear operator. Since its discovery it has evolved into a pivotal tool used across diverse disciplines, including physics, chemistry, and engineering. Over the past 25 years, the Magnus expansion has undergone significant mathematical developments which revealed an intricate interplay between algebra, combinatorics, and geometry. By emphasizing a modern perspectives based on the use of pre- and post-Lie algebras, we discuss the Magnus expansion from the viewpoint of the notion of crossed morphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16674 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | What is the Magnus Expansion? Ebrahimi-Fard, Kurusch Mencattini, Igor Quesney, Alexandre Mathematical Physics Rings and Algebras 16S30, 16T30, 17A30 The Magnus expansion, introduced by Wilhelm Magnus in 1954, is an infinite Lie series employed to express solutions for first-order homogeneous linear differential equations involving a linear operator. Since its discovery it has evolved into a pivotal tool used across diverse disciplines, including physics, chemistry, and engineering. Over the past 25 years, the Magnus expansion has undergone significant mathematical developments which revealed an intricate interplay between algebra, combinatorics, and geometry. By emphasizing a modern perspectives based on the use of pre- and post-Lie algebras, we discuss the Magnus expansion from the viewpoint of the notion of crossed morphism. |
| title | What is the Magnus Expansion? |
| topic | Mathematical Physics Rings and Algebras 16S30, 16T30, 17A30 |
| url | https://arxiv.org/abs/2312.16674 |