Ternary Hom–Nambu–Lie algebras induced by Hom–Lie algebras
Ternary Hom–Nambu–Lie algebras induced by Hom–Lie algebras
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DOI：
10.1063/1.3359004
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发表时间：
2009-12
影响因子：
1.3
通讯作者：
J. Arnlind;A. Makhlouf;S. Silvestrov
中科院分区：
文献类型：
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作者：
J. Arnlind;A. Makhlouf;S. Silvestrov
考虑 n 元代数结构、推广李代数和泊松代数的需要在物理学中变得越来越重要，因此研究与 n 元代数相关的数学概念应该很有趣。本文的目的是研究由 Hom-Lie 代数、线性扭曲映射和满足某些兼容性条件的迹函数的二元乘法构造的三元乘法（作为 n-Lie 结构的变形）。我们证明了扭曲映射的核与迹函数之间的关系在这种情况下起着重要作用，并提供了使用这种结构获得的 Hom-Nambu-Lie 代数的例子。
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.