A Relative Theory for Leibniz n-Algebras

In this paper we show that for a $n$-Filippov algebra $\text{g},$ the tensor power ${\text{g}}^{\otimes n-1}$ is endowed with a structure of anti-symmetric co-representation over the Leibniz algebra ${\text{g}}^{\wedge n-1}$. 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.