Skew-Hom-Lie algebras in Semi-Euclidean spaces

2024/10/27 by Zhen Xiong, Xiong, Zhen
Mathematics · #17B99 #51P05 #Advanced Topics in Algebra #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2410.20414

openalex publication_date 2024/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 (R⁴₂,[⋅,⋅]_θ,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 [⋅,⋅]_θ and P.

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