Geometry and classifications of some $ω$-Lie algebras
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908903302758400 |
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| author | Chen, Yin Ren, Shan Zhang, Runxuan |
| author_facet | Chen, Yin Ren, Shan Zhang, Runxuan |
| contents | Using group actions and orbit-stabilizer methods, we study the geometry of isomorphism classes of finite-dimensional $ω$-Lie algebras over a field $\mathbb{K}$ of characteristic $\neq 2$ and establish a one-to-one correspondence between the set of isomorphism classes and the orbit space of a stabilizer of $ω$. We also apply techniques from computational ideal theory to explore the geometric structure of the affine variety of all 3-dimensional $ω$-Lie algebras over $\mathbb{K}$, showing that this variety is a 6-dimensional irreducible affine variety and a complete intersection. As an application, we derive a complete classification of all 3-dimensional $ω$-Lie algebras over an algebraically closed field of characteristic $\neq 2$, up to $ω$-Lie algebra isomorphism. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_20417 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometry and classifications of some $ω$-Lie algebras Chen, Yin Ren, Shan Zhang, Runxuan Rings and Algebras 17A30, 17D99, 13P25 Using group actions and orbit-stabilizer methods, we study the geometry of isomorphism classes of finite-dimensional $ω$-Lie algebras over a field $\mathbb{K}$ of characteristic $\neq 2$ and establish a one-to-one correspondence between the set of isomorphism classes and the orbit space of a stabilizer of $ω$. We also apply techniques from computational ideal theory to explore the geometric structure of the affine variety of all 3-dimensional $ω$-Lie algebras over $\mathbb{K}$, showing that this variety is a 6-dimensional irreducible affine variety and a complete intersection. As an application, we derive a complete classification of all 3-dimensional $ω$-Lie algebras over an algebraically closed field of characteristic $\neq 2$, up to $ω$-Lie algebra isomorphism. |
| title | Geometry and classifications of some $ω$-Lie algebras |
| topic | Rings and Algebras 17A30, 17D99, 13P25 |
| url | https://arxiv.org/abs/2603.20417 |