| 腾文,游泰杰.Lie-Yamaguti着色代数的导子与形变[J].数学研究及应用,2022,42(1):15~30 |
| Lie-Yamaguti着色代数的导子与形变 |
| Derivations and Deformations of Lie-Yamaguti Color Algebras |
| 投稿时间：2020-12-25 修订日期：2021-05-20 |
| DOI：10.3770/j.issn:2095-2651.2022.01.003 |
| 中文关键词: Lie-Yamaguti着色代数 表示 上同调 导子 形变 |
| 英文关键词:Lie-Yamaguti color algebra representation cohomology derivations deformations |
| 基金项目:国家自然科学基金(Grant No.11761017),贵州省科技厅基金(Grant No.[2020]1Y005). |
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| 中文摘要: |
| 本文引入了Lie-Yamaguti着色代数的表示和上同调. 其次, 引入Lie-Yamaguti着色代数的广义导子及性质. 最后, 研究Lie-Yamaguti着色代数的线性形变, 并引入了Lie-Yamaguti着色代数上的Nijenhuis算子的概念,它可以生成一个平凡的形变. |
| 英文摘要: |
| In this paper, we introduce the representation and cohomology theory of Lie-Yamaguti color algebras. Furthermore, we introduce the notions of generalized derivations of Lie-Yamaguti color algebras and present some properties. Finally, we study linear deformations of Lie-Yamaguti color algebras, and introduce the notion of a Nijenhuis operator on a Lie-Yamaguti color algebra, which can generate a trivial deformation. |
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