The geometric constraints on Filippov algebroids
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916181094432768 |
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| author | Bi, Yanhui Chen, Zhixiong Chen, Zhuo Xiang, Maosong |
| author_facet | Bi, Yanhui Chen, Zhixiong Chen, Zhuo Xiang, Maosong |
| contents | Filippov n-algebroids are introduced by Grabowski and Marmo as a natural generalization of Lie algebroids. On this note, we characterized Filippov n-algebroid structures by considering certain multi-input connections, which we called Filippov connections, on the underlying vector bundle. Through this approach, we could express the n-ary bracket of any Filippov n-algebroid using a torsion-free type formula. Additionally, we transformed the generalized Jacobi identity of the Filippov n-algebroid into the Bianchi-Filippov identity. Furthermore, in the case of rank n vector bundles, we provided a characterization of linear Nambu-Poisson structures using Filippov connections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_04180 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The geometric constraints on Filippov algebroids Bi, Yanhui Chen, Zhixiong Chen, Zhuo Xiang, Maosong Rings and Algebras Differential Geometry 53C15, 57R22 Filippov n-algebroids are introduced by Grabowski and Marmo as a natural generalization of Lie algebroids. On this note, we characterized Filippov n-algebroid structures by considering certain multi-input connections, which we called Filippov connections, on the underlying vector bundle. Through this approach, we could express the n-ary bracket of any Filippov n-algebroid using a torsion-free type formula. Additionally, we transformed the generalized Jacobi identity of the Filippov n-algebroid into the Bianchi-Filippov identity. Furthermore, in the case of rank n vector bundles, we provided a characterization of linear Nambu-Poisson structures using Filippov connections. |
| title | The geometric constraints on Filippov algebroids |
| topic | Rings and Algebras Differential Geometry 53C15, 57R22 |
| url | https://arxiv.org/abs/2309.04180 |