Contact and 2-compatible Lie algebras
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917464893292544 |
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| author | Remm, Elisabeth |
| author_facet | Remm, Elisabeth |
| contents | A $n$-dimensional Lie algebra $g=(V,μ)$ is called $2$-compatible if it is isomorphic to a quadratic deformation of a Lie algebra $g_0=(V,μ_0)$. By quadratic deformation we means a formal deformation $μ_t=μ_0+tφ_1+t^2φ_2$ where $μ_t$ is a Lie algebra on $V \otimes K[[t]]$. It is equivalent to say that we have the following system $\sum_{i+j \leq 4} φ_i \circ φ_j= 0$. This notion naturally appears in the theory of classification of contact Lie algebras because any $(2p+1)$-dimensional contact Lie algebra is isomorphic to a quadratic deformation of the Heisenberg algebra $\mathcal{H}_{2p+1}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_05131 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Contact and 2-compatible Lie algebras Remm, Elisabeth Rings and Algebras Differential Geometry 17A30- 17B05 - 17B08- 53D10 A $n$-dimensional Lie algebra $g=(V,μ)$ is called $2$-compatible if it is isomorphic to a quadratic deformation of a Lie algebra $g_0=(V,μ_0)$. By quadratic deformation we means a formal deformation $μ_t=μ_0+tφ_1+t^2φ_2$ where $μ_t$ is a Lie algebra on $V \otimes K[[t]]$. It is equivalent to say that we have the following system $\sum_{i+j \leq 4} φ_i \circ φ_j= 0$. This notion naturally appears in the theory of classification of contact Lie algebras because any $(2p+1)$-dimensional contact Lie algebra is isomorphic to a quadratic deformation of the Heisenberg algebra $\mathcal{H}_{2p+1}$. |
| title | Contact and 2-compatible Lie algebras |
| topic | Rings and Algebras Differential Geometry 17A30- 17B05 - 17B08- 53D10 |
| url | https://arxiv.org/abs/2605.05131 |