Homology with coefficients of Leibniz n-algebras

Co-representations of Leibniz n-algebras are defined as left modules over the universal enveloping algebra. We define the homology of a Leibniz it-algebra L with coefficients in a co-representation M as the homology of the Leibniz complex of L circle times n-1 over the co-representation M circle times L. We prove the cancellation of the homology over free objects and the generalization of the following isomorphism in Leibniz homology HL*(L, L) congruent to HL*+1 (L, K) from Leibniz algebras to Leibniz n-algebras. To cite this article: J.M. Casas, C. R. Acad. Sci. Paris, Ser. I 347 (2009). (C) 2009 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.