Abstract
In this paper, the equivalence of central extensions and H α , α V 3 T , V is proven in the study in Hom- δ -Jordan Lie triple systems. The concepts of Nijenhuis operators of Hom- δ -Jordan Lie triple systems are given. Moreover, a trivial deformation is got.
Highlights
It is well known that Lie triple systems are closely related to geometry
The definitions of the semisimplicity, radicality, and solvability for Lie triple systems are discussed, and the simple Lie triple system is determined by Lister [1]
Kubo and Taniguchi showed that in Lie triple systems, this kind of cohomology plays an important role in the study of deformations and extensions in 2004 [3]
Summary
It is well known that Lie triple systems are closely related to geometry. In a symmetric space, its tangent algebra is a Lie triple system. Cohomologies of Lie triple systems were obtained [2]. Kubo and Taniguchi showed that in Lie triple systems, this kind of cohomology plays an important role in the study of deformations and extensions in 2004 [3]. Later, generalized derivations of Hom-Lie triple systems were determined [18]. We pay our main attention to consider central extensions and Nijenhuis operators of Hom-δ-Jordan Lie triple systems. The capital letter F denotes an arbitrary field
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