Homological Algebra
Homology with coefficients of Leibniz n-algebras
Comptes Rendus. Mathématique, Volume 347 (2009) no. 11-12, pp. 595-598.

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 Ln1 over the co-representation ML.

We prove the cancellation of the homology over free objects and the generalization of the following isomorphism in Leibniz homology HL(L,L)HL+1(L,K) from Leibniz algebras to Leibniz n-algebras.

Les co-représentations des n-algèbres de Leibniz sont définies comme les modules à gauche sur l'algèbre enveloppante universelle. Nous définissons l'homologie de la n-algèbre de Leibniz L à coefficients dans une co-représentation M comme l'homologie du complexe de Leibniz de Ln1 sur la co-représentation ML.

Nous démontrons l'annulation de l'homologie sur les objets libres et nous généralisons l'isomorphisme HL(L,L)HL+1(L,K) des algèbres de Leibniz aux n-algèbres de Leibniz.

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DOI: 10.1016/j.crma.2009.04.004
Casas, José Manuel 1

1 Dpto. Matemática Aplicada I, Univ. de Vigo, 36005 Pontevedra, Spain
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Casas, José Manuel. Homology with coefficients of Leibniz n-algebras. Comptes Rendus. Mathématique, Volume 347 (2009) no. 11-12, pp. 595-598. doi : 10.1016/j.crma.2009.04.004. http://www.numdam.org/articles/10.1016/j.crma.2009.04.004/

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