Poincaré-Birkhoff-Witt theorem for Leibniz \(n\)-algebras

DOI10.1016/j.jsc.2007.05.003zbMath1131.17001OpenAlexW2046119161WikidataQ123026257 ScholiaQ123026257MaRDI QIDQ2466872

Manuel Ladra Gonzalez, Manuel Avelino Insua Hermo, José Manuel Casas Mirás

Publication date: 16 January 2008

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2007.05.003

zbMATH Keywords

Gröbner basesuniversal enveloping algebraLeibniz algebraLeibniz \(n\)-algebraPoincaré-Birkhoff-Witt theorem

Mathematics Subject Classification ID

Computational aspects of associative rings (general theory) (16Z05) Leibniz algebras (17A32) Computational methods for problems pertaining to nonassociative rings and algebras (17-08) Other (n)-ary compositions ((n ge 3)) (17A42)

Related Items (6)

3-Lie∞-algebras and 3-Lie 2-algebras ⋮ Universal Associative Envelopes of (n+ 1)-Dimensionaln-Lie Algebras ⋮ On classification problem of Loday algebras ⋮ Homology with coefficients of Leibniz \(n\)-algebras ⋮ Split regular Hom-Leibniz color 3-algebras ⋮ Test for Leibniz \(n\)-algebra structure

Uses Software

• NCAlgebra

Cites Work

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• Leibniz n-algebras
• On the Representation Theory of Lie Triple Systems
• Cohomology of Lie Triple Systems and Lie Algebras With Involution
• Generalized Hamiltonian Dynamics
• Leibniz algebroid associated with a Nambu-Poisson structure
• Lie and Jordan Triple Systems
• A Structure Theory of Lie Triple Systems

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