Rota-Baxter operators on $ω$-Lie algebras
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866908844481839104 |
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| author | Chen, Yin Ren, Shan Shan, Jiawen Zhang, Runxuan |
| author_facet | Chen, Yin Ren, Shan Shan, Jiawen Zhang, Runxuan |
| contents | This article explores Rota-Baxter operators on finite-dimensional $ω$-Lie algebras over a field of characteristic not 2. We provide several methods for constructing left-symmetric algebras, $ω$-Lie algebras, and Hom-Lie algebras via compatible Rota-Baxter operators on a given $ω$-Lie algebra. We also study the geometric structures of compatible Rota-Baxter operators of weight $0$ and isometric Rota-Baxter operators of weight $1$ over the field of complex numbers. In particular, we prove that the affine variety of all isometric Rota-Baxter operators of weight $1$ on any finite-dimensional non-Lie complex simple $ω$-Lie algebra is $1$-dimensional. Furthermore, we show that for every $4$-dimensional non-Lie complex $ω$-Lie algebra, there always exists a nilpotent compatible Rota-Baxter operator of weight $0$ such that the induced Hom-Lie algebra is nonabelian but solvable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_18413 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rota-Baxter operators on $ω$-Lie algebras Chen, Yin Ren, Shan Shan, Jiawen Zhang, Runxuan Rings and Algebras 17B38, 13P25, 17B61, 17D30 This article explores Rota-Baxter operators on finite-dimensional $ω$-Lie algebras over a field of characteristic not 2. We provide several methods for constructing left-symmetric algebras, $ω$-Lie algebras, and Hom-Lie algebras via compatible Rota-Baxter operators on a given $ω$-Lie algebra. We also study the geometric structures of compatible Rota-Baxter operators of weight $0$ and isometric Rota-Baxter operators of weight $1$ over the field of complex numbers. In particular, we prove that the affine variety of all isometric Rota-Baxter operators of weight $1$ on any finite-dimensional non-Lie complex simple $ω$-Lie algebra is $1$-dimensional. Furthermore, we show that for every $4$-dimensional non-Lie complex $ω$-Lie algebra, there always exists a nilpotent compatible Rota-Baxter operator of weight $0$ such that the induced Hom-Lie algebra is nonabelian but solvable. |
| title | Rota-Baxter operators on $ω$-Lie algebras |
| topic | Rings and Algebras 17B38, 13P25, 17B61, 17D30 |
| url | https://arxiv.org/abs/2602.18413 |