Compatible root graded anti-pre-Lie algebraic structures on finite-dimensional complex simple Lie algebras
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909542776832000 |
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| author | Bai, Chengming Gao, Dongfang |
| author_facet | Bai, Chengming Gao, Dongfang |
| contents | We investigate the compatible root graded anti-pre-Lie algebraic structures on any finite-dimensional complex simple Lie algebra by the representation theory of ${\rm sl_2(\C)}$. We show that there does not exist a compatible root graded anti-pre-Lie algebraic structure on a finite-dimensional complex simple Lie algebra except ${\rm sl_2(\C)}$, whereas there is exactly one compatible root graded anti-pre-Lie algebraic structure on ${\rm sl_2(\C)}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15241 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Compatible root graded anti-pre-Lie algebraic structures on finite-dimensional complex simple Lie algebras Bai, Chengming Gao, Dongfang Quantum Algebra Rings and Algebras Representation Theory 17B10, 17B65, 17B66, 17B68, 17B70 We investigate the compatible root graded anti-pre-Lie algebraic structures on any finite-dimensional complex simple Lie algebra by the representation theory of ${\rm sl_2(\C)}$. We show that there does not exist a compatible root graded anti-pre-Lie algebraic structure on a finite-dimensional complex simple Lie algebra except ${\rm sl_2(\C)}$, whereas there is exactly one compatible root graded anti-pre-Lie algebraic structure on ${\rm sl_2(\C)}$. |
| title | Compatible root graded anti-pre-Lie algebraic structures on finite-dimensional complex simple Lie algebras |
| topic | Quantum Algebra Rings and Algebras Representation Theory 17B10, 17B65, 17B66, 17B68, 17B70 |
| url | https://arxiv.org/abs/2503.15241 |