Hom-李代数的广义导子

周佳, 牛艳君, 陈良云

数学学报 ›› 2015, Vol. 58 ›› Issue (4) : 551-558.

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数学学报 ›› 2015, Vol. 58 ›› Issue (4) : 551-558. DOI: 10.12386/A2015sxxb0056
论文

Hom-李代数的广义导子

    周佳1, 牛艳君2,3, 陈良云2,3
作者信息 +

Generalized Derivations of Hom-Lie Algebras

    Jia ZHOU1, Yan Jun NIU2,3, Liang Yun CHEN2,3
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文章历史 +

摘要

给出Hom-李代数L的广义导子代数、拟导子代数和中心导子代数的一些基本性质.进一步地, 有GDer(L) = QDer(L) + QC(L). 同时,得到QDer(L)可以嵌入并成为一个更大的 Hom-李代数的导子.

Abstract

We give some basic properties of the generalized derivation algebra, quasiderivation algebra and center derivation algebra of a Hom-Lie Algebra L. Moreover, we prove that GDer(L) = QDer(L) + QC(L). We also prove that QDer(L) can be embedded as derivations in a larger Hom-Lie algebra.

关键词

Hom-李代数 / 广义导子 / 拟导子 / 型心

Key words

Hom-Lie algebras / generalized derivations / quasiderivations / centroids

引用本文

导出引用
周佳, 牛艳君, 陈良云. Hom-李代数的广义导子. 数学学报, 2015, 58(4): 551-558 https://doi.org/10.12386/A2015sxxb0056
Jia ZHOU, Yan Jun NIU, Liang Yun CHEN. Generalized Derivations of Hom-Lie Algebras. Acta Mathematica Sinica, Chinese Series, 2015, 58(4): 551-558 https://doi.org/10.12386/A2015sxxb0056

参考文献

[1] Abdaoui K., Ammar F., Makhlouf A., Constructions and cohomology of color Hom-Lie algebras, arXiv: 1307. 2612.

[2] Benoist Y., La partie semi-simple de l'algèbre des dérivations d'une algèbre de Lie nilpotente, C. R. Acad, 1988, 307: 901-904.

[3] Chen L., Ma Y., Ni L., Generalized derivations of Lie color algebras, Results. Math., 2013, 63: 923-936.

[4] Gohr A., On Hom-algebras with surjective twisting, J. Algebra, 2010, 324(7): 1438-1491.

[5] Hartwig J., Larsson D., Silvestrov S., Deformations of Lie algebras using σ-derivations, J. Algebra, 2006, 295: 321-344.

[6] Leger G. F., Luks E. M., Generalized derivations of Lie algebras, J. Algebra, 2000, 228: 165-203.

[7] Melville D. J., Centroids of nilpotent Lie algebras, Comm. Algebra, 1992, 20: 3649-3682.

[8] Sheng Y., Representations of Hom-Lie Algebras, Algebr. Represent. Theory, 2012, 15(6): 1081-1098.

[9] Yau D., Hom-quantum groups: I, Quasi-triangular Hom-bialgebras, J. Phys. A, 2012, 45(6): 065203, 23pp.

[10] Yau D., The Hom-Yang-Baxter equation and Hom-Lie algebras, J. Math. Phys., 2011, 52(5): 053502, 19pp.

基金

国家自然科学基金资助项目(11171055, 11471090);吉林农业大学青年基金资助项目(201329)

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