Cohomology of a restricted Lie algebra with a restricted derivation in characteristic 2
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909222077202432 |
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| author | Mao, Dan Chen, Liangyun |
| author_facet | Mao, Dan Chen, Liangyun |
| contents | This paper mainly studies the ResLieDer pair in characteristic 2, that is, a restricted Lie algebra with a restricted derivation. We define the restricted representation of a ResLieDer pair and the corresponding cohomology complex. We show that a ResLieDer pair is rigid if the second cohomology group is trivial and a deformation of order $n$ is extensible if and only if its obstruction class is trivial. Moreover, we prove that the central extensions of a ResLieDer pair are classified by the second cohomology group. Finally, we show that a pair of restricted derivations is extensible if and only if its obstruction class is trivial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07552 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cohomology of a restricted Lie algebra with a restricted derivation in characteristic 2 Mao, Dan Chen, Liangyun Rings and Algebras This paper mainly studies the ResLieDer pair in characteristic 2, that is, a restricted Lie algebra with a restricted derivation. We define the restricted representation of a ResLieDer pair and the corresponding cohomology complex. We show that a ResLieDer pair is rigid if the second cohomology group is trivial and a deformation of order $n$ is extensible if and only if its obstruction class is trivial. Moreover, we prove that the central extensions of a ResLieDer pair are classified by the second cohomology group. Finally, we show that a pair of restricted derivations is extensible if and only if its obstruction class is trivial. |
| title | Cohomology of a restricted Lie algebra with a restricted derivation in characteristic 2 |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2406.07552 |