李color代数上的积结构和复结构  

Product Structures and Complex Structures on Lie Color Algebras

作　　者：王聪[1] 侯莹 陈良云[1] WANG Cong;HOU Ying;CHEN Liangyun(School of Mathematics and Statistics,Northeast Normal University,Changchun 130024,China)

机构地区：[1]东北师范大学数学与统计学院,长春130024

出　　处：《海南热带海洋学院学报》2021年第5期37-48,共12页Journal of Hainan Tropical Ocean University

基　　金：国家自然科学基金项目(11771069;12071405)。

摘　　要：本文研究了李color代数上的积结构和复结构,给出了李color代数上积结构和复结构存在的充要条件以及它们之间的关系,并给出了一些特殊的积结构和复结构。作为应用,引入伪黎曼度量概念,把伪黎曼度量和积结构、伪黎曼度量和复结构结合起来分别刻画了李color代数上的Para-Kahler结构和Kahler结构。The present study on the product structures and complex structures on Lie color algebras gave the necessary and sufficient conditions for the existence of product structures and complex structures on Lie color algebras and their relations,and some special product structure and complex structure as well.As an application,by introducing the concept of pseudo Riemannian metric and combining pseudo Riemannian metric with product structure and pseudo Riemannian metric with complex structure,the Para-Kahler structures and Kahler structures on Lie color algebras were described respectively.

关 键 词：李color代数 积结构 复结构 Para-Kahler结构 Kahler结构 

分 类 号：O152.5[理学—数学]