Ternary Hom–Nambu–Lie algebras induced by Hom–Lie algebras

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 multiplicat...

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Bibliographic Details
Published in:Journal of mathematical physics 2010-04, Vol.51 (4), p.043515-043515-11
Main Authors: Arnlind, Joakim, Makhlouf, Abdenacer, Silvestrov, Sergei
Format: Article
Language:English
Subjects:
Algebra
Exact sciences and technology
Lie groups
Matematik
matematik/tillämpad matematik
Mathematical methods in physics
Mathematical models
Mathematics
Mathematics/Applied Mathematics
Natural Sciences
Naturvetenskap
Physics
Poisson distribution
Sciences and techniques of general use
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Summary: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.
ISSN:0022-2488
1089-7658
1089-7658
DOI:10.1063/1.3359004