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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.05041 |
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| _version_ | 1866908536188960768 |
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| author | Jiang, Jun Sheng, Yunhe Sun, Geyi |
| author_facet | Jiang, Jun Sheng, Yunhe Sun, Geyi |
| contents | In this paper, first we use the higher derived brackets to construct an $L_\infty$-algebra, whose Maurer-Cartan elements are $3$-Lie algebra morphisms. Using the differential in the $L_\infty$-algebra that govern deformations of the morphism, we give the cohomology of a $3$-Lie algebra morphism. Then we study the rigidity and stability of $3$-Lie algebra morphisms using the established cohomology theory. In particular, we show that if the first cohomology group is trivial, then the morphism is rigid; if the second cohomology group is trivial, then the morphism is stable. Finally, we study the stability of $3$-Lie subalgebras similarly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05041 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability and rigidity of 3-Lie algebra morphisms Jiang, Jun Sheng, Yunhe Sun, Geyi Rings and Algebras In this paper, first we use the higher derived brackets to construct an $L_\infty$-algebra, whose Maurer-Cartan elements are $3$-Lie algebra morphisms. Using the differential in the $L_\infty$-algebra that govern deformations of the morphism, we give the cohomology of a $3$-Lie algebra morphism. Then we study the rigidity and stability of $3$-Lie algebra morphisms using the established cohomology theory. In particular, we show that if the first cohomology group is trivial, then the morphism is rigid; if the second cohomology group is trivial, then the morphism is stable. Finally, we study the stability of $3$-Lie subalgebras similarly. |
| title | Stability and rigidity of 3-Lie algebra morphisms |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2409.05041 |