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arXiv · 2410.20414

Skew-Hom-Lie algebras in Semi-Euclidean spaces

Zhen Xiong
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Abstract

In this paper, first we introduce the notion of a skew-Hom-Lie algebra and give some examples. Then we study their representations and give the coboundary operator of skew-Hom-Lie algebras. As an application, there have a skew-Hom-Lie algebra $(R^4_2,[\cdot,\cdot]_\theta,P)$ in semi-Euclidean spaces. For the null space of Semi-Euclidean spaces, there have a subset $V^*$ of the null space, and $V^*$ is invariant under the actions of $[\cdot,\cdot]_\theta$ and $P$.

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Zhen Xiong. 2024-10-27. Skew-Hom-Lie algebras in Semi-Euclidean spaces. https://arxiv.org/abs/2410.20414

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