| A. Nourou ISSA.On Quadratic Left Leibniz Algebras and Related Lie-Yamaguti Structures[J].数学研究及应用,2025,45(2):152~162 |
| On Quadratic Left Leibniz Algebras and Related Lie-Yamaguti Structures |
| On Quadratic Left Leibniz Algebras and Related Lie-Yamaguti Structures |
| 投稿时间：2024-08-26 修订日期：2024-12-02 |
| DOI：10.3770/j.issn:2095-2651.2025.02.002 |
| 中文关键词: Leibniz algebra $T^*$-extension Lie-Yamaguti algebra |
| 英文关键词:Leibniz algebra $T^*$-extension Lie-Yamaguti algebra |
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| 摘要点击次数: 100 |
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| 中文摘要: |
| A left Leibniz algebra equipped with an invariant nondegenerate skew-symmetric bilinear form (i.e., a skew-symmetric quadratic Leibniz algebra) is constructed. The notion of $T^*$-extension of Lie-Yamaguti algebras is introduced and it is observed that the trivial extension of a Lie-Yamaguti algebra is a quadratic Lie-Yamaguti algebra. It is proved that every symmetric (resp., skew-symmetric) quadratic Leibniz algebra induces a quadratic (resp., symplectic) Lie-Yamaguti algebra. |
| 英文摘要: |
| A left Leibniz algebra equipped with an invariant nondegenerate skew-symmetric bilinear form (i.e., a skew-symmetric quadratic Leibniz algebra) is constructed. The notion of $T^*$-extension of Lie-Yamaguti algebras is introduced and it is observed that the trivial extension of a Lie-Yamaguti algebra is a quadratic Lie-Yamaguti algebra. It is proved that every symmetric (resp., skew-symmetric) quadratic Leibniz algebra induces a quadratic (resp., symplectic) Lie-Yamaguti algebra. |
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