Generalized derivations of n-Hom Lie superalgebras
Generalized derivations of n-Hom Lie superalgebras
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发表时间：
2014-06
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通讯作者：
J. Zhou;Liangyun Chen;Yao Ma
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作者：
J. Zhou;Liangyun Chen;Yao Ma
众所周知，n-Hom李超代数是n-Lie代数的某些推广。研究了乘法n-Hom李超代数的广义导子。我们将Leger和Luks的主要结果推广到了乘法n-Hom李超代数的情形。首先，我们回顾了与乘法n-Hom李超代数N$相关的一些概念。进一步给出了广义导子、拟导子、中心导子、质心和拟质心的定义。显然，我们有下面的塔$ZDer（N）\subseteq Der（N）\subseteq QDer（N）\subseteq GDer（N）\subseteq End（N）$。随后，我们给出了这些导子之间的一些有用的性质和联系。此外，我们还得到了$N$的拟导子可以作为导子嵌入到一个较大的乘法n-Hom李超代数中.最后，我们得到了当$N$的中心等于零时，较大的乘法n-Hom李超代数的导子具有直和分解的结论。
It is well known that n-Hom Lie superalgebras are certain generalizations of n-Lie algebras. This paper is devoted to investigate the generalized derivations of multiplicative n-Hom Lie superalgebras. We generalize the main results of Leger and Luks to the case of multiplicative n-Hom Lie superalgebras. Firstly, we review some concepts associated with a multiplicative n-Hom Lie superalgebra $N$. Furthermore, we give the definitions of the generalized derivations, quasiderivations, center derivations, centroids and quasicentroids. Obviously, we have the following tower $ZDer(N)\subseteq Der(N)\subseteq QDer(N)\subseteq GDer(N)\subseteq End(N)$. Later on, we give some useful properties and connections between these derivations. Moreover, we obtain that the quasiderivation of $N$ can be embedded as a derivation in a larger multiplicative n-Hom Lie superalgebra. Finally, we conclude that the derivation of the larger multiplicative n-Hom Lie superalgebra has a direct sum decomposition when the center of $N$ is equal to zero.