Journal of Lie Theory 24 (2014), No. 4, 909--929
Copyright Heldermann Verlag 2014
Notes on Cohomologies of Lie Triple Systems
Tao Zhang
College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, P. R. China
zhangtaozata@gmail.com
The cohomology theory of Lie triple systems in the sense of Yamaguti is studied by means of cohomology of Leibniz algebras in the sense of Loday. The notion of Nijenhuis operators for Lie triple systems is introduced to describe trivial deformations. We also study the abelian extensions of Lie triple systems in details.
Keywords: Lie triple systems, cohomology, deformations, Nijenhuis operators, abelian extensions.
MSC: 17A40, 17A30, 17B56
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