一类五维李代数的交叉模
Crossed Modules of a Class of Five-Dimensional Lie Algebras
DOI: 10.12677/PM.2019.93035, PDF,    国家自然科学基金支持
作者: 王玉玫：上海大学理学院，上海
关键词: 五维李代数；交叉模；三阶相对上同调；Five-Dimensional Lie Algebra； Crossed Module； Third Relative Cohomology
摘要: 文[1]主要研究了四维不可解李代数的交叉模的等价类集和三阶相对上同调群。在此基础上，本文研究了一类五维李代数的交叉模的性质，并确定出其等价类的条件，从而证明了这类五维李代数的三阶相对上同调群不是平凡的。
Abstract: The set of equivalence classes of crossed modules of four-dimensional unsolvable Lie algebras and the third relative cohomology groups were studied in [1]. Based on this work, the present paper will study the crossed modules of a certain five-dimensional Lie algebra and determine the condition of its equivalent class. Furthermore, it is shown that the third relative cohomology group of the five-dimensional Lie algebra is not trivial.
文章引用：王玉玫. 一类五维李代数的交叉模[J]. 理论数学, 2019, 9(3): 270-275. https://doi.org/10.12677/PM.2019.93035

参考文献

[1] 王圣祥, 谭玉明. 四维李代数的交叉模和三阶上同调群[J]. 西安工程大学学报, 2009, 23(4): 146-149.
[2] Whitehead, J.H.C. (1949) Combinatorial Homotopy II. Bulletin of the American Mathematical Society, 55, 453-496.
[Google Scholar] [CrossRef] 
[3] Gerstenhaber, M. (1966) On the Deformation of Rings and Algebras: II. Annals of Mathematics, 84, 1-19.
[Google Scholar] [CrossRef] 
[4] Kassel, C. and Loday, J.L. (1982) Extensions centrales d’algèbres de Lie. Annales de l’institut Fourier (Grenoble), 32, 119-142.
[Google Scholar] [CrossRef] 
[5] 王圣祥, 马先超. Virasoro代数的交叉模[J]. 西安工程大学学报, 2008, 22(4): 510-512.
[6] 王圣祥, 周建华. 李代数的交叉模[J]. 东南大学学报(自然科学版), 2009, 39(1): 185-190.
[7] Wagemann, F. (2006) On Lie Algebra Crossed Modules. Communications in Algebra, 34, 1699-1722.
[Google Scholar] [CrossRef] 

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