| 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
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| 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). |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2022.02.009 |
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