Unified products for Leibniz algebras. Applications

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• 作者：A.L. Agore ; G. Militaru
• 关键词：17A32 ; 17B05 ; 17B56
• 刊名：Linear Algebra and its Applications
• 出版年：2013
• 出版时间：1 November, 2013
• 年：2013
• 卷：439
• 期：9
• 页码：2609-2633
• 全文大小：449 K

文摘

Let be a Leibniz algebra and E a vector space containing as a subspace. All Leibniz algebra structures on E containing as a subalgebra are explicitly described and classified by two non-abelian cohomological type objects: provides the classification up to an isomorphism that stabilizes and will classify all such structures from the view point of the extension problem - here V is a complement of 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 of Leibniz algebras are given as a converse of the factorization problem. They are classified by another cohomological object denoted by , where is the canonical matched pair associated to a given complement . Several examples are worked out in details.