Symmetric Biderivations on Complex Semisimple Lie Algebras
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911948343345152 |
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| author | Shiyuan, Liu Dong, Liu Yueqiang, Zhao |
| author_facet | Shiyuan, Liu Dong, Liu Yueqiang, Zhao |
| contents | This paper studies biderivations on finite-dimensional complex semisimple Lie algebras to their finite-dimensional modules. More precisely, we prove that all such symmetric biderivations are trivial. As applications, we determine all biderivations on Takiff algebras and symplectic oscillator algebras, as well as all supersymmetric biderivations over some Lie superalgebras including all finite-dimensional classical simple Lie superalgebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05581 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symmetric Biderivations on Complex Semisimple Lie Algebras Shiyuan, Liu Dong, Liu Yueqiang, Zhao Representation Theory This paper studies biderivations on finite-dimensional complex semisimple Lie algebras to their finite-dimensional modules. More precisely, we prove that all such symmetric biderivations are trivial. As applications, we determine all biderivations on Takiff algebras and symplectic oscillator algebras, as well as all supersymmetric biderivations over some Lie superalgebras including all finite-dimensional classical simple Lie superalgebras. |
| title | Symmetric Biderivations on Complex Semisimple Lie Algebras |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2407.05581 |