Central Extensions and Deformations of Lie Triple Systems with a Derivation
Received:December 29, 2020  Revised:April 28, 2021
Key Words: Lie triple system   derivation   representation   cohomology   central extension   deformation  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.12161013) and the General Project of Guizhou University of Finance and Economics (Grant No.2021KYYB16).
Author NameAffiliation
Shuangjian GUO School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guizhou 550025, P. R. China 
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      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.
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