具有导子的李三系的中心扩张与形变

Central Extensions and Deformations of Lie Triple Systems with a Derivation

中文关键词:  李三系  导子  表示  上同调  中心扩张  形变

英文关键词:Lie triple system  derivation  representation  cohomology  central extension  deformation

中文摘要:

      考虑具有导子的李三系.由李三系和一个导子称为LietsDer对.定义系数在表示中的LietsDer对的上同调理论.研究LietsDer对的中心扩张.接下来,将形变理论推广到由李三系和导子构成LietsDer对上,它由带有系数的LietsDer对的上同调所支配.

英文摘要:

      In this paper, we consider Lie triple systems with derivations. A pair consisting of a Lie triple system and a distinguished derivation is called a LietsDer pair. We define a cohomology theory for LietsDer pair with coefficients in a representation. We study central extensions of a LietsDer pair. In the next, we generalize the formal deformation theory to LietsDer pairs in which we deform both the Lie triple system bracket and the distinguished derivation. It is governed by the cohomology of LietsDer pair with coefficients in itself.