On crossed modules of pre-Lie algebras
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910472980135936 |
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| author | Luo, Xuedan |
| author_facet | Luo, Xuedan |
| contents | Given a Lie algebra $\mathfrak g$ and a $\mathfrak{g}$-module $V$, it is due to Gerstenhaber that there is an isomorphism between $H^3(\mathfrak{g}, V )$ and the group of equivalence classes of crossed modules with kernel $V$ and cokernel $\mathfrak {g}$. The goal of this article is to obtain this result for pre-Lie algebras and their modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03149 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On crossed modules of pre-Lie algebras Luo, Xuedan Representation Theory Rings and Algebras Given a Lie algebra $\mathfrak g$ and a $\mathfrak{g}$-module $V$, it is due to Gerstenhaber that there is an isomorphism between $H^3(\mathfrak{g}, V )$ and the group of equivalence classes of crossed modules with kernel $V$ and cokernel $\mathfrak {g}$. The goal of this article is to obtain this result for pre-Lie algebras and their modules. |
| title | On crossed modules of pre-Lie algebras |
| topic | Representation Theory Rings and Algebras |
| url | https://arxiv.org/abs/2406.03149 |