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The purpose of this paper is to study the relationships between a Hom-Jordan algebras and its induced ternary Hom-Jordan algebras. We give some properties of the αk-generalized derivation algebra G D e r (J) of a ternary Hom-Jordan algebras. In particular, we prove that G D e r (J) = Q D e r (J) + Q Γ (J) , the sum of the αk-quasiderivation algebra and the αk-quasicentroid. We also prove that Q D e r (J) can be embedded as derivations in a larger ternary Hom-Jordan algebras. General results on αk-centroids of ternary Hom-Jordan algebras are also developed in the paper. [ABSTRACT FROM AUTHOR]

The study of n -Lie algebras which are natural generalization of Lie algebras is motivated by Nambu Mechanics and recent developments in String Theory and M-branes. The purpose of this paper is to define cohomology complexes and study deformation theory of n -Lie algebra morphisms. We discuss infinitesimal deformations, equivalent deformations and obstructions. Moreover, we provide various examples. [ABSTRACT FROM AUTHOR]