A Relative Theory for Leibniz n-Algebras

Abstract

In this paper we show that for an n-Filippov algebra 𝔤, the tensor power 𝔤⊗n-1 is endowed with a structure of anti-symmetric co-representation over the Leibniz algebra 𝔤∧n-1. This co-representation is used to define some 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.