On -Jordan Lie triple systems

Central Extensions and Nijenhuis Operators of Hom- δ -Jordan Lie Triple Systems

“…Particularly, Dðt 1 , t 2 Þðt 3 Þ = δ½t 1 , t 2 , t 3 and ( 5), (6), and (7) hold, if V = T, A = α, and θðt 1 , t 2 Þðt 3 Þ = ½t 3 , t 1 , t 2 . In this case, T is called the adjoint ðT, ½•, • , • , αÞ-module and θ is called the adjoint representation of ðT, ½•, • , • , αÞ on itself with respect to α.…”

“…Then, they obtained a method to construct simple Jordan superalgebras by certain triple systems and studied the F-type Jordan superalgebra of a Jordan Lie triple system [5]. Recently, the cohomologies, Nijenhuis operators, representations, abelian extensions, and T * -extensions of δ-Jordan Lie triple systems were developed by Ma and Chen [6].…”

Restricted δ Lie Triple Systems

“…Peng Jianrong gives the generalized derivation of δ Lie three systems [8]. Cohomological characterizations of δ -Jordan Lie triple systems are established, then deformations, Nijenhuis operators, Abelian extensions and T * -extensions of δ -Jordan Lie triple systems are studied using cohomology [9]. Liu Yanpei gives the structural properties limiting the Lie three systems [10].…”

Derivations and Deformations of δ-Jordan Lie Supertriple Systems

“…Later, Kamiya and Okubo [14] studied a construction of simple Jordan superalgebras from certain triple systems. Recently, Ma and Chen [7] discussed the cohomology theory, the deformations, Nijenhuis operators, abelian extensions and T * -extensions of δ-Jordan Lie triple system.…”

“…In Section 5, we study Nijenhuis operators for a δ-Jordan Lie supertriple system to describe trivial deformations.Remark 2.2. Clearly, T 0 is an ordinary δ-Jordan Lie triple system in [7]. Especially, the case of δ = 1 defines a Lie supertriple system while the other case of δ = −1 may be termed an anti Lie supertriple system as in [9].…”