Central extensions and deformations of Hom-Lie triple systems |
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| Authors: | Yao Ma Jie Lin |
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| Institution: | 1. School of Mathematics and Statistics, Northeast Normal University, Changchun, China;2. Sino-European Institute of Aviation Engineering, Civil Aviation University of China, Tianjin, China |
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| Abstract: | In this paper, we study the cohomology theory of Hom-Lie triple systems generalizing the Yamaguti cohomology theory of Lie triple systems. We introduce the central extension theory for Hom-Lie triple systems and show that there is a one-to-one correspondence between equivalent classes of central extensions of Hom-Lie triple systems and the third cohomology group. We develop the 1-parameter formal deformation theory of Hom-Lie triple systems and prove that it is governed by the cohomology group. |
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| Keywords: | Central extension cohomology deformation Hom-Lie triple system |
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