JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (10): 1-5.doi: 10.6040/j.issn.1671-9352.0.2021.684

   

On Abelian extensions of Hom-δ-Jordan Lie triple systems

MA Li-li, WU Di, LI Qiang, XU Jing   

  1. School of Science, Qiqihar University, Qiqihar 161006, Heilongjiang, China
  • Published:2022-10-06

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Abstract: Cohomology theory of Hom-δ-Jordan Lie triple systems is introduced. The 3-cocycle is obtained by the section of Hom-δ-Jordan Lie triple systems. The structure of a Hom-δ-Jordan Lie triple system is given using representations and 3-cocycles. Sufficient and necessary condition for the equivalence of Abelian extensions of Hom-δ-Jordan Lie triple systems is shown.

Key words: Hom-δ-Jordan Lie triple system, 3-cocycle, Abelian extension

CLC Number: 

  • O152.5
[1] YAU D. On n-ary Hom-Nambu and Hom-Nambu-Lie algebras[J]. Journal of Geometry and Physics, 2012, 62(2):506-522.
[2] ZHOU Jia, CHEN Liangyun, MA Yao. Generalized derivations of Hom-Lie triple systems[J]. Bulletin of the Malaysian Mathematical Sciences Society, 2018, 41:637-656.
[3] MA Yao, CHEN Liangyun, LIN Jie. Central extensions and deformations of Hom-Lie triple systems[J]. Communications in Algebra, 2018, 46(3):1212-1230.
[4] CHEN Liangyun, YI Yang, CHEN Ming, et al. Cohomology and 1-parameter formal deformations of Hom-δ-Lie triple systems[J]. Advances in Applied Clifford Algebras, 2019, 29:1-14.
[5] MA Lili, CHEN Liangyun. On δ-Jordan Lie triple systems[J]. Linear and Multilinear Algebra, 2017, 65(4):731-751.
[6] 李强,马丽丽,田巍.关于δ-Jordan李三系的交换扩张[J]. 东北师大学报(自然科学版),2018,50(2):7-10. LI Qiang, MA Lili, TIAN Wei. On Abelian extensions of δ-Jordan Lie triple systems[J]. Journal of Northeast Normal University(Natural Science Edition), 2018, 50(2):7-10.
[7] 马丽丽,戴迪,李强.δ-Jordan李超三系的构造和交换扩张[J]. 山东大学学报(理学版), 2021, 56(8):76-80. MA Lili, DAI Di, LI Qiang. Constitutions and Abelian extensions of δ-Jordan Lie supertriple systems[J]. Journal of Shandong University(Natural Science), 2021, 56(8):76-80.
[1] MA Li-li, DAI Di, LI Qiang. Constitutions and Abelian extensions of δ-Jordan Lie supertriple systems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(8): 76-80.
[2] TENG Wen, JIN Jiu-lin, YOU Tai-jie. Linear deformations and Abelian extensions of Lie supertriple systems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(4): 14-19.
[3] MA Li-li, LI Qiang. Abelian extensions of δ-Lie color algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(8): 38-42.
[4] LI Qiang, MA Li-li, WANG Xiao-yan, LYU Li-jiao. Abelian extensions of Hom-Jordan Lie algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(12): 4-8.
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