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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

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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