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arXiv · 2401.08592

Double Extensions of Multiplicative Restricted Hom-Lie Algebras

Dan Mao·Zeyu Hao·Liangyun Chen
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Abstract

In this paper, we study the double extension of a restricted quadratic Hom-Lie algebra $(V,[\cdot,\cdot]_{V},\alpha_{V},B_{V})$, 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.

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Dan Mao, Zeyu Hao, Liangyun Chen. 2023-11-17. Double Extensions of Multiplicative Restricted Hom-Lie Algebras. https://arxiv.org/abs/2401.08592

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