Künneth-style formula for the homology of Leibniz algebras
type: Item
instance of: scholarly article
title: Künneth-style formula for the homology of Leibniz algebras
zbMATH Open document ID: 0880.17001
DOI: 10.1007/BF02622097
author: J.-L. Loday
published in: Mathematische Zeitschrift
publication date: 1998-02-11T00:00:00Z
full work available at URL: https://eudml.org/doc/174832
review text: The paper concerns Leibniz algebras. The author points to the work [\textit{J.-L. Loday}, Enseign. Math., II. Sér. 39, 269-293 (1993; Zbl 0806.55009)] for a review on more information on these objects. The aim of this successive work by the author examining these algebras is to compute \(HL_*({\mathfrak g}\oplus {\mathfrak g}')\), i.e. the Leibniz homology of the direct sum of Leibniz algebras \({\mathfrak g}\) and \({\mathfrak g}'\). The author gets a Künneth-type formula \[ HL_*({\mathfrak g}\oplus{\mathfrak g}')\cong HL_*({\mathfrak g})*HL_*({\mathfrak g}') \] in which the right-hand side represents a sort of noncommutative tensor product for graded modules.
Mathematics Subject Classification ID: 17A32
Mathematics Subject Classification ID: 17B55
Mathematics Subject Classification ID: 18G60
Mathematics Subject Classification ID: 55U99
zbMATH DE Number: 861932
zbMATH Keywords: Künneth formula
zbMATH Keywords: Leibniz algebras
zbMATH Keywords: Leibniz homology
Wikidata QID: Q123348975
reviewed by: Jan Kubarski
MaRDI profile type: Publication
cites work: Homologie et cohomologie des algèbres de Lie
cites work: A noncommutative version of Lie algebras: Leibniz algebras
cites work: Universal enveloping algebras of Leibniz algebras and (co)homology
description: scientific article; zbMATH DE number 861932