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Ternary Hom–Nambu–Lie algebras induced by Hom–Lie algebras
Max Planck Institute for Gravitational Physics (AEI), Am Mühlenberg 1, D-14476 Golm, Germany.ORCID iD: 0000-0002-8727-2169
Laboratoire de Mathématiques, Informatique et Applications, Université de Haute Alsace, 4, rue des Frères Lumière, F-68093 Mulhouse, France .
Centre for Mathematical Sciences, Lund University, Box 118, SE-221 00 Lund, Sweden .
2010 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 51, 043515-1-043515-11 p., 43515Article in journal (Refereed) Published
Abstract [en]

The need to consider n  -ary algebraic structures, generalizing Lie and Poisson algebras, has become increasingly important in physics, and it should therefore be of interest to study the mathematical concepts related to n  -ary algebras. The purpose of this paper is to investigate ternary multiplications (as deformations of n  -Lie structures) constructed from the binary multiplication of a Hom–Lie algebra, a linear twisting map, and a trace function satisfying certain compatibility conditions. We show that the relation between the kernels of the twisting maps and the trace function plays an important role in this context and provide examples of Hom–Nambu–Lie algebras obtained using this construction.

Place, publisher, year, edition, pages
American Institute of Physics (AIP), 2010. Vol. 51, 043515-1-043515-11 p., 43515
National Category
Mathematics Algebra and Logic
Identifiers
URN: urn:nbn:se:liu:diva-122353DOI: 10.1063/1.3359004OAI: oai:DiVA.org:liu-122353DiVA: diva2:865807
Available from: 2015-10-29 Created: 2015-10-29 Last updated: 2015-11-09

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Arnlind, Joakim
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