Unified products for Leibniz algebras. Applications

Ana Agore, Gigel Militaru

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)


Let g be a Leibniz algebra and E a vector space containing g as a subspace. All Leibniz algebra structures on E containing g as a subalgebra are explicitly described and classified by two non-abelian cohomological type objects: HL2g (V, g) provides the classification up to an isomorphism that stabilizes g and HL2 (V, g) will classify all such structures from the view point of the extension problem - here V is a complement
of g in E. A general product, called the unified product, is introduced as a tool for our approach. The crossed (resp. bicrossed) products between two Leibniz algebras are introduced as special cases of the unified product: the first one is responsible for the extension problem while the bicrossed product is responsible for the factorization problem. The description and the classification of all complements of a given extension g E of Leibniz algebras are given as a converse of the factorization problem. They are
classified by another cohomological object denoted by HA2(h, g |. Several examples are worked out in details.
Original languageEnglish
Pages (from-to)2609-2633
JournalLinear Algebra and its Applications
Issue number9
Publication statusPublished - 2013


  • The extension and the factorization problem
  • non-abelian cohomology for Leibniz algebras


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