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| 摘要: |
| 本文研究了李color三系的上同调结构和Nijenhuis算子的问题.利用李三系的上同调和Nijenhuis算子的研究方法,构造出李color三系的上边界算子,获得了李color三系的单参数形式形变.推广了线性映射生成无穷小形变的充分必要条件,同时证明了由一个李color三系的Nijenhuis算子产生的形变是平凡的. |
| 关键词: 李color三系 表示 上同调 形变 Nijenhuis算子 |
| DOI： |
| 分类号:O152.5 |
| 基金项目:国家自然科学基金资助 (11801121); 黑龙江省自然科学基金资助 (QC2018006); 黑龙江省普通高校基本科研业务费资助 (LGYC2018JC002). |
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| COHOMOLOGY AND NIJENHUIS OPERATORS OF LIE COLOR SYSTEMS |
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ZHANG Wan-ying,CAO Yan
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| Abstract: |
| In this paper, we study the cohomology structure and the Nijenhuis operator of the Lie color triple systems. Using the cohomology of the Lie triple systems and the study of the Nijenhuis operator, the upper boundary operator of the Lie color triple systems is constructed, and the one-parameter formal deformation of the Lie color triple systems is given. The su±cient and necessary conditions for linear maps to generate infinitesimal transformations are generalized, while the deformation produced by the Nijenhuis operator of a Lie color triple systems is proved to be trivial. |
| Key words: Lie color triple system representation cohomology deformation Nijenhuis operator |
