Hom-李三系上的乘积结构和复结构

doi:10.6040/j.issn.1671-9352.9.2021.008

摘要/Abstract

摘要： 本文主要从代数角度研究Hom-李三系上的两种几何结构,即积结构、复结构。分别给出了积结构和复结构存在时对应的Hom-李三系的分解。同时,也研究了一些特殊的积结构和复结构。最后,在这两种结构间增加一个兼容条件,得到了复积结构。

关键词: Hom-李三系, Hom-Nijenhuis算子, 积结构, 复结构, 复积结构

Abstract: This paper mainly studies two geometric structures on Hom-Lie triple system from the perspective of algebra, named product structure and complex structure. The decomposition of Hom-Lie triple system corresponding to the existence of product structure and complex structure is given respectively. At the same time, some special product structures and complex structures are also studied. Finally, adding a compatibility condition between the two structures in order to obtain the complex product structure.

Key words: Hom-Lie triple system, Hom-Nijenhuis operator, product structure, complex structure, complex product structure

中图分类号:

O152.5

陈良云,侯莹,马瑶. Hom-李三系上的乘积结构和复结构[J]. 《山东大学学报(理学版)》, 2021, 56(10): 48-60.

CHEN Liang-yun, HOU Ying, MA Yao. Product and complex structures on Hom-Lie triple systems[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(10): 48-60.

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