JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (12): 4-8.doi: 10.6040/j.issn.1671-9352.0.2018.059

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Abelian extensions of Hom-Jordan Lie algebras

LI Qiang, MA Li-li, WANG Xiao-yan, LYU Li-jiao   

  1. School of Science, Qiqihar University, Qiqihar 161006, Heilongjiang, China
  • Online:2018-12-20 Published:2018-12-18

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Abstract: Using representations of Hom-Jordan Lie algebras T, the sufficient and necessary conditions of constructing Hom-Jordan Lie algebra T⊕V are obtained. The equivalent abelian extensions of Hom-Jordan Lie algebras giving the same representation is proved. A 2-cocycle by a section of the abelian extension is obtained.

Key words: Hom-Jordan Lie algebra, representation, 2-cocycle, abelian extension

CLC Number: 

  • O152.55
[1] OKUBO S, KAMIYA N. Jordan-Lie superalgebra and Jordan-Lie triple system[J]. Journal of Algebra, 1997, 198(2):388-411.
[2] QIAN Ling, ZHOU Jia, CHEN Liangyun. Engel theorem of Jordan Lie algebra and its applications[J]. Chinese Annals of Mathematics Series A, 2012, 33A(5):517-526.
[3] HARTWIG J, LARSSON D, SILVESTROV S. Deformations of Lie algebras using σ-derivations[J]. Journal of Algebra, 2006, 295(2):314-361.
[4] SHENG Yunhe. Representations of Hom-Lie algebras[J]. Algebras and Representation Theory, 2012, 15(6):1081-1098.
[5] LARSSON D, SILVESTROV S. Quasi-Hom-Lie algebras, central extensions and 2-cocycle-like identities[J]. Journal of Algebra, 2005, 288(2):321-344.
[6] LIU Yan, CHEN Liangyun, MA Yao. Hom-Nijienhuis operators and T*-extensions of Hom-Lie superalgebras[J]. Linear Algebra and its Applications, 2013, 439(7):2131-2144.
[7] ABDAOUI K, AMMAR F, MAKHLOUF A. Constructions and cohomology of Hom-Lie color algebras[J]. Communications in Algebra, 2015, 43(11):4581-4612.
[8] MA Lili, CHEN Liangyun, ZHAO Jun. δ-Hom-Jordan Lie superalgebras[J]. Communications in Algebra, 2018, 46(4):1668-1697.
[9] ZHAO Jun, CHEN Liangyun, MA Lili. Representations and T*-extensions of Hom-Jordan-Lie algebras[J]. Communications in Algebra, 2016, 44(7):2786-2812.
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