一类新的Hom-李代数

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摘要本文在Long模范畴中定义了一类新的Hom-李代数,通过Hom-结合代数和扭曲映射分别给出构造方法。作为应用,在三维线性空间上和三维Heisenberg李代数上分别构造了Hom-李代数结构。

作者陈雯雯

机构地区滁州学院数学与金融学院

出处《滁州学院学报》 2021年第2期49-53,57,共6页 Journal of Chuzhou University

基金安徽省自然科学基金项目“张量范畴上Ribbon结构的构造、分类及应用”(1908085MA03) 安徽省高等学校自然科学研究一般项目“特定子图存在性的极值问题研究”(KJ2020B05)

关键词 Hom-李代数 Hom-结合代数 Long模范畴 Heisenberg李代数

参考文献1

1Loday, J. L., Pirashvili, T.: Universal enveloping algebras of Leibniz algebras and (co)homology. Math. Ann., 296, 139-158 (1993).
2Hartwig, J., Larsson, D., Silvestrov, S.: Deformations of Lie algebras using a-derivation. J. Algebra, 295, 314 361 (2006).
3Makhlouf, A., Silvestrov, S.: Notes on formal deformations of Horn-associative and Horn-Lie algebras. Forum Math., 22(4), 715 739 (2010).
4Gao, Y.: The second Leibniz homology group for Kac-Moody Lie algebras. Bull. Lond. Math. Soc., 32, 25-33 (2000).
5Gao, Y.: Leibniz homology of unitary Lie algebras. J. Pure Appl. Algebra, 140, 33 56 (1999).
6Wang, Q., Tan, S.: Leibniz central extension on a Block Lie algebra. Algebra CoUoq., 14(4), 713-720 (2007).
7Liu, D., Lin, L.: On the toroidal Leibniz algebras. Acta Mathematica Sinica, English Series, 24(2), 227-240 (2008).
8Yau, D.: Horn-algebras as deformations and homology. J. Lie Theory, 19, 409-421 (2009).
9Loday, J. L.: Dialgebras, Lecture Notes in Mathematics, Vol. 1763, Springer, 2001, 7-66.
10Casas, J., Datuashvili, T.: Noncommutative Leibniz-Poission algebras. Comm. Algebra, 34, 2507-2530 (2006).

1张永平,王欣彦.Hom-Leibniz代数的直和[J].沈阳化工大学学报,2014,28(2):181-183.
2Shengxiang WANG,Xiaohui ZHANG.On the Structures of Hom-Lie Algebras[J].Journal of Mathematical Research with Applications,2014,34(4):459-466.
3张永平,鲁亚男,王欣彦.Hom-Leibniz代数的导子[J].沈阳化工大学学报,2014,28(4):374-376.
4SHEN Zhen-jun WEI Zhu ZHANG Qing-cheng.Hom-Leibniz Superalgebras[J].Chinese Quarterly Journal of Mathematics,2014,29(4):583-591.
5Yongsheng CHENG,Guang-ai SONG.Corepresentation and Categorical Realization of Dual Hom-Quasi-Hopf Algebras[J].Journal of Mathematical Research with Applications,2015,35(2):157-171.
6尹彦彬,刘玲,陈敏茹.关于Hom-Leibniz代数胚表示[J].河南大学学报（自然科学版）,2015,45(4):390-394.
7CHENG Yong-sheng,LIU Guo-jing.Monoidal Category Approach to Dual Hom-quasi-Hopf Algebras[J].Chinese Quarterly Journal of Mathematics,2015,30(2):218-226. 被引量：2
8Yongsheng CHENG,Xiufu ZHANG.Representations and categorical realization of Hom-quasi-Hopf algebras[J].Frontiers of Mathematics in China,2015,10(6):1263-1281.
9亓欢歌,程永胜,王梦平,武琳丽.Kac Determinant Formula for the q-deformed Virasoro Algebra of Hom-type[J].Chinese Quarterly Journal of Mathematics,2016,31(4):331-339. 被引量：1
10周佳,赵昕,张宇.Hom-Leibniz代数的广义导子[J].吉林大学学报（理学版）,2017,55(2):195-200. 被引量：2

滁州学院学报

2021年第2期

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