JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (4): 14-19.doi: 10.6040/j.issn.1671-9352.0.2020.517

Previous Articles    

Linear deformations and Abelian extensions of Lie supertriple systems

TENG Wen1,2, JIN Jiu-lin1, YOU Tai-jie1*   

  1. 1. School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, Guizhou, China;
    2. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, Guizhou, China
  • Published:2021-04-13

Abstract: Firstly, Lie supertriple systems structure is characterized by using two order linear deformations. It leads to a definition of Nijenhuis operators. Secondly, a representation and a cocycle are constructed as a tool to get the Abelian extensions of the Lie supertriple system.

Key words: Lie supertriple system, linear deformation, Nijenhuis operator, Abelian extension

CLC Number: 

  • O152.5
[1] BONDY J A, MURTY U S R. Graph theory with applications[M]. New York: Macmilan Ltd Press, 1976.
[2] OKUBO S. Parastatistics as Lie-supertriple systems[J]. J Math Phy, 1994, 35(6):2785-2803.
[3] OKUBO S, KAMIYA N. A construction of simple Jordan superalgebra of F type from a Jordan-Lie triple system[J]. Ann Mat Pura Appl, 2002, 181(3):339-348.
[4] OKUBO S, KAMIYA N. Quasi-classical Lie super algebras and Lie supertriple systems[J]. Comm Algebra, 2002, 30(8):3825-3850.
[5] ZHANG Zhixue, JIA Peipei. The Killing forms and decomposition theorems of Lie supertriple systems[J]. Acta Math Sin, 2009, 29(2):360-370.
[6] 张知学, 刘文丽, 贾培佩.关于单李超三系的分类[J].数学进展, 2011, 40(3):293-298. ZHANG Zhixue, LIU Wenli, JIA Peipei. On the classification of simple Lie supertriple systems[J]. Advances In Mathematics, 2011, 40(3):293-298.
[7] 林洁, 陈良云, 汪金燕. 关于可解李超三系[J]. 数学年刊(A辑), 2009, 30(4):505-516. LIN Jie, CHEN Liangyun, WANG Jinyan. On solvable Lie triple supersystems[J]. Chinese Annals of Mathematics, 2009, 30(4):505-516.
[8] 林洁, 陈良云, 杨吉. 一类李超三系的构造[J]. 东北师大学报(自然科学版), 2009,41(1):6-9. LIN Jie, CHEN Liangyun, YANG Ji. A constitution of Lie supertriple[J]. Journal of Northeast Normal University(Natural Science Edition), 2009, 41(1):6-9.
[9] 马瑶, 陈良云, 刘东. 李超三系的广义导子[J].数学学报(中文版), 2013, 56(6):961-970. MA Yao, CHEN Liangyun. On generalized derivations of Lie supertriple systems[J]. Acta Mathematics Sinica(Chinese Series), 2013, 56(6):961-970.
[10] PENG Jianrong, CHEN Liangyun, SUN Bing. Centroids of Lie supertriple systems[J/OL]. Adv Math Phy, 2015, 2015: 1-9. https://doi.org/10.1155/2015/949046
[11] 潘玉霞, 张庆成. 李超三系的分解唯一性[J]. 数学物理学报, 2008(6):1058-1066. PAN Yuxia, ZHANG Qingcheng. The uniqueness of the decomposition of Lie supertriple systems[J]. Acta Mathematica Scientia, 2008(6):1058-1066.
[12] 唐鑫鑫, 刘宁, 张庆成. 李超三系上带有权λ的导子[J]. 吉林大学学报(理学版), 2017, 55(4):797-803. TANG Xinxin, LIU Ning, ZHANG Qingcheng. Derivations of weight λ on Lie supertriple systems[J]. Journal of Jinlin University(Science Edition), 2017,55(4):797-803.
[13] 郭双建. 李超三系的上同调和Nijenhuis算子[J]. 华东师范大学学报(自然科学版), 2020(4):1-11. GUO Shuangjian. Cohomology and Nijenhuis operators of Lie supertriple systems[J]. Journal of East China Normal University(Natural Science), 2020(4):1-11.
[1] MA Li-li, LI Qiang. Abelian extensions of δ-Lie color algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(8): 38-42.
[2] 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.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!