Homology with coefficients of Leibniz n-algebras

Abstract

Co-representations of Leibniz n-algebras are defined as left modules over the universal enveloping algebra. We define the homology of a Leibniz n-algebra L with coefficients in a co-representation M as the homology of the Leibniz complex of L⊗ n - 1 over the co-representation M ⊗ L. We prove the cancellation of the homology over free objects and the generalization of the following isomorphism in Leibniz homology H L{star operator} (L, L) ≅ H L{star operator} + 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). © 2009 Académie des sciences.