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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2203.07001 |
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| _version_ | 1866912029475864576 |
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| author | Lebedev, Alexei Leites, Dimitry |
| author_facet | Lebedev, Alexei Leites, Dimitry |
| contents | The Amitsur--Levitzki identity for matrices was generalized in several directions: by Kostant for simple finite-dimensional Lie algebras, by Kirillov (later joined by Kontsevich, Molev, Ovsienko, and Udalova) for simple vectorial Lie algebras with polynomial coefficients, and by Gie, Pinczon, and Ushirobira for the orthosymplectic Lie superalgebra $\mathfrak{osp}(1|n)$. Dzhumadildaev switched the focus of attention in these results by considering the algebra formed by antisymmetrizors and discovered a hidden supersymmetry of commutators. We overview these results and their possible generalizations (open problems). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_07001 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Dzhumadildaev brackets: a hidden supersymmetry of commutators and the Amitsur-Levitzki--type identities Lebedev, Alexei Leites, Dimitry Representation Theory 17B01 The Amitsur--Levitzki identity for matrices was generalized in several directions: by Kostant for simple finite-dimensional Lie algebras, by Kirillov (later joined by Kontsevich, Molev, Ovsienko, and Udalova) for simple vectorial Lie algebras with polynomial coefficients, and by Gie, Pinczon, and Ushirobira for the orthosymplectic Lie superalgebra $\mathfrak{osp}(1|n)$. Dzhumadildaev switched the focus of attention in these results by considering the algebra formed by antisymmetrizors and discovered a hidden supersymmetry of commutators. We overview these results and their possible generalizations (open problems). |
| title | The Dzhumadildaev brackets: a hidden supersymmetry of commutators and the Amitsur-Levitzki--type identities |
| topic | Representation Theory 17B01 |
| url | https://arxiv.org/abs/2203.07001 |