Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras

We present a procedure to construct (n+1)-Hom-Nambu-Lie algebras from n-Hom-Nambu-Lie algebras equipped with a generalized trace function. It turns out that the implications of the compatibility conditions, that are necessary for this construction, can be understood in terms of the kernel of the trace function and the range of the twisting maps. Furthermore, we investigate the possibility of defining (n+k)-Lie algebras from n-Lie algebras and a k-form satisfying certain conditions.