Double Extensions of Multiplicative Restricted Hom-Lie Algebras
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911759349055488 |
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| author | Mao, Dan Hao, Zeyu Chen, Liangyun |
| author_facet | Mao, Dan Hao, Zeyu Chen, Liangyun |
| contents | In this paper, we study the double extension of a restricted quadratic Hom-Lie algebra $(V,[\cdot,\cdot]_{V},α_{V},B_{V})$, which is an enlargement of $V$ by means of a central extension and a restricted derivation $\mathscr{D}$. In particular, we prove that the double extension of a restricted quadratic Hom-Lie algebra $V$ with a $\mathscr{D}$-invariant bilinear form $B_{V}$ is restricted. Conversely, any irreducible restricted quadratic Hom-Lie algebra with nonzero center is proved to be the double extension of another restricted quadratic Hom-Lie algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_08592 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Double Extensions of Multiplicative Restricted Hom-Lie Algebras Mao, Dan Hao, Zeyu Chen, Liangyun Rings and Algebras In this paper, we study the double extension of a restricted quadratic Hom-Lie algebra $(V,[\cdot,\cdot]_{V},α_{V},B_{V})$, which is an enlargement of $V$ by means of a central extension and a restricted derivation $\mathscr{D}$. In particular, we prove that the double extension of a restricted quadratic Hom-Lie algebra $V$ with a $\mathscr{D}$-invariant bilinear form $B_{V}$ is restricted. Conversely, any irreducible restricted quadratic Hom-Lie algebra with nonzero center is proved to be the double extension of another restricted quadratic Hom-Lie algebra. |
| title | Double Extensions of Multiplicative Restricted Hom-Lie Algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2401.08592 |