Homology with coefficients of Leibniz \(n\)-algebras
type: Item
instance of: scholarly article
title: Homology with coefficients of Leibniz \(n\)-algebras
zbMATH Open document ID: 1173.17003
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2009-06-10T00:00:00Z
review text: The author continues study of the (co)homology of Leibniz \(n\)-algebras developed in [\textit{J. M. Casas, J.-L. Loday} and \textit{T. Pirashvili}, Forum Math. 14, No. 2, 189--207 (2002; Zbl 1037.17002)]. In this paper he defines the notion of a corepresentation of a Leibniz \(n\)-algebra \(L\) and the homology group \(_nHL_*(L,M)\) of \(L\) with coefficient in a corepresentation \(M\). If \(n=2\), or \(M\) is a trivial corepresentation, then one obtains known groups.
Mathematics Subject Classification ID: 17A32
Mathematics Subject Classification ID: 17B55
zbMATH DE Number: 5563758
zbMATH Keywords: Leibniz algebras
zbMATH Keywords: Leibniz homology
zbMATH Keywords: \(n\)-fold algebras
Wikidata QID: Q123195239
author: J. M. Casas
reviewed by: Teimuraz Pirashvili
MaRDI profile type: Publication
full work available at URL: j.crma.2009.04.004
OpenAlex ID: W2014034872
cites work: Homology with Trivial Coefficients of Leibnizn-Algebras
cites work: Poincaré-Birkhoff-Witt theorem for Leibniz \(n\)-algebras
cites work: Leibniz \(n\)-algebras.
cites work: Algèbres de Leibnitz : définitions, propriétés
cites work: Suite spectrale d'une extension d'algèbres de Leibniz
cites work: Cohomology of lie algebras in the tensor category of linear maps
cites work: A noncommutative version of Lie algebras: Leibniz algebras
cites work: Universal enveloping algebras of Leibniz algebras and (co)homology
DOI: 10.1016/J.CRMA.2009.04.004
description: scientific article; zbMATH DE number 5563758