  In this paper we show that for a $n$-Filippov algebra $\g,$ the tensor power
$\g^{\otimes n-1}$ is endowed with a structure of anti-symmetric
co-representation over the Leibniz algebra $\g^{\wedge n-1}$. This
co-representation is used to define two relative theories for Leibniz
$n$-algebras with $n>2$ and obtain exact sequences relating them. As a result,
we construct a spectral sequence for the Leibniz homology of Filippov algebras.

K-Theory and Homology;Rings and Algebras