李color代数上的积结构和复结构

Product Structures and Complex Structures on Lie Color Algebras

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.