着色李超代数与左着色对称结构

LIE COLOR ALGEBRAS AND COLOR LEFT-SYMMETRIC STRUCTURES

本文研究了着色李超代数上的左着色对称结构问题.利用着色李超代数的两种仿射表示和1-上同调群,得出左着色对称结构存在的几个充分或必要条件,推广了文[2]的结论.

In this paper, we study the left color symmetric structures on Lie color algebras. By using two kinds of affine representations of Lie color algebras and the first cohomology group, we obtain some necessary or sufficient conditions to the problem whether there is any left color sysmmetric structure on a given Lie color algebra which generalize the result of [2].