发表机构
Shiraz University; Mälardalen University（设拉子大学; 马尔默达尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究乘法n元Hom-Nambu超代数的完备性，建立相关判据，给出非n元Hom-Lie超代数的完备例子，分析直和、扭曲下中心性质及低维分类中的完备成员。
AI 中文摘要
我们引入并研究乘法n元Hom-Nambu超代数的完备性。由于n元Hom-Nambu括号未必完全超反对称，我们将其中心定义为各位置中心的交集。当乘法n元Hom-Nambu超代数的中心为平凡，且对所有k≥0，每个α^(k+1)-导子都是内导子时，该超代数是完备的。我们证明此概念可归约为乘法n元Hom-Lie超代数的通常完备性；此外，针对具有零扭曲映射的满射括号，我们建立了完备性判据，并给出一个非n元Hom-Lie超代数的完备n元Hom-Nambu超代数。我们还研究了完备n元Hom-Lie超代数的直和及扭曲下中心的性质。最后，从乘法Hom-Lie超代数出发，我们考虑递归诱导的乘法n元Hom-Nambu超代数，当扭曲映射为满射时，证明此构造中中心的平凡性得以保留和反映；我们还发现每个二元α^k-导子均满足诱导括号对应的相对α^k-导子恒等式，并确定了所选低维Hom-Lie超代数与3-Hom-Lie超代数分类中的完备成员。
英文摘要
We introduce and study completeness for multiplicative $n$-ary Hom-Nambu superalgebras. Because an $n$-ary Hom-Nambu bracket is not necessarily totally super-skew-symmetric, we define its center as the intersection of its positional centers. A multiplicative $n$-ary Hom-Nambu superalgebra is complete when its center is trivial, and every $α^{k+1}$-derivation is inner for all $k \geq 0$. We show that this notion reduces to the usual completeness for multiplicative $n$-Hom-Lie superalgebras. Furthermore, we establish a completeness criterion for surjective brackets with a zero twisting map and provide a complete $n$-ary Hom-Nambu superalgebra that is not an $n$-Hom-Lie superalgebra. We also study the direct sums of complete $n$-Hom-Lie superalgebras and the behavior of centers under twisting. Finally, starting from a multiplicative Hom-Lie superalgebra, we consider recursively induced multiplicative $n$-ary Hom-Nambu superalgebras. When the twisting map is surjective, we prove that triviality of the center is preserved and reflected in this construction. We also observe that every binary $α^k$-derivation satisfies the corresponding relative $α^k$-derivation identity for the induced bracket. Finally, we determine the complete members in the selected low-dimensional Hom-Lie and $3$-Hom-Lie superalgebra classifications.
Comments43 pages
