Homology, Homotopy and Applications

Homology and central extensions of Leibniz and Lie n-algebras

José Manuel Casas, Emzar Khmaladze, Manuel Ladra, and Tim Van der Linden

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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.

Article information

Source
Homology Homotopy Appl., Volume 13, Number 1 (2011), 59-74.

Dates
First available in Project Euclid: 29 July 2011

Permanent link to this document
https://projecteuclid.org/euclid.hha/1311953346

Mathematical Reviews number (MathSciNet)
MR2803867

Zentralblatt MATH identifier
1287.17004

Subjects
Primary: 17A32: Leibniz algebras 18E99: None of the above, but in this section 18G10: Resolutions; derived functors [See also 13D02, 16E05, 18E25] 18G50: Nonabelian homological algebra

Keywords
Semi-abelian category higher central extension higher Hopf formula homology Leibniz $n$-algebra Lie $n$-algebra

Citation

Casas, José Manuel; Khmaladze, Emzar; Ladra, Manuel; Van der Linden, Tim. Homology and central extensions of Leibniz and Lie n-algebras. Homology Homotopy Appl. 13 (2011), no. 1, 59--74. https://projecteuclid.org/euclid.hha/1311953346


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