Homology, Homotopy and Applications

Volume 13 (2011)

Number 1

Homology and central extensions of Leibniz and Lie $n$-algebras

Pages: 59 – 74

DOI: https://dx.doi.org/10.4310/HHA.2011.v13.n1.a3

Authors

José Manuel Casas (Departamento de Matemática Aplicada I, Universidad de Vigo, Pontevedra, Spain)

Emzar Khmaladze (Department of Algebra, A. Razmadze Mathematical Institute, Tbilisi, Republic of Georgia; Departamento de Matemática Aplicada I, Universidad de Vigo, Pontevedra, Spain)

Manuel Ladra (Departamento de Álgebra, Universidad de Santiago de Compostela, Spain)

Tim Van der Linden (Centro de Matemática, Universidade de Coimbra, Portugal; Institut de recherche en mathématique et physique, Université catholique de Louvain, Louvain-la-Neuve, Belgium)

Abstract

From the viewpoint of semi-abelian homology, some recent results on homology of Leibniz $n$-algebras can be explained categorically. In parallel with these results, we develop an analogous theory for Lie $n$-algebras. We also consider the relative case: homology of Leibniz $n$-algebras relative to the subvariety of Lie $n$-algebras.

Keywords

semi-abelian category, higher central extension, higher Hopf formula, homology, Leibniz $n$-algebra, Lie $n$-algebra

2010 Mathematics Subject Classification

17A32, 18Exx, 18G10, 18G50

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Published 12 July 2011