三维Gel’fand-Dorfman双代数分类
Classification of Three-Dimensional Gel'fand-Dorfman Bialgebras
摘要
利用Lie代数的自同构给出三维Gel’fand-Dorfman双代数的一个完全分类.
We applied the automorphisms of Lie algebras to classifying the three-dimensional Gel＇fand-Dorfman bialgebras.
出处
《吉林大学学报（理学版）》
CAS
CSCD
北大核心
2013年第6期1019-1022,共4页
Journal of Jilin University:Science Edition
基金
国家自然科学基金(批准号:10871057
11171055)
参考文献12
-
1Jacobson N. Lie Algebras [M]. New York: Interscience-Wiley, 1962.
-
2Osborn J. Novikov Algebras [J]. Nova J Algebra Geom, 1992(1) : 1-14.
-
3BAI Cheng ming, MENG Dao-ji. The Classification of Novikov Algebras in l.ow Dimensions [J]. J Phys A; Math Gen, 2001, 34(8): 1581-1594.
-
4KANG Yi-fang, CHEN Zhi-qi. Novikov Superalgebras in Low Dimensions [J]. J Nonlinear Math Phys, 2009, 16:251-257.
-
5ZHUFu-hai, CHEN Zhi-qi. NovikovSuperalgebras withA0=A1A1 [J]. Cze Math J, 2010, 60(4): 903-907.
-
6Gel'land I M, Dorfman Y I. Hamiltonian Operators and Algebraic Structures Related to Them [J]. Funkts Anal Its Prilozhen, 1979, 13(4): 248-262.
-
7XU Xiao-ping. Quadratie Conformal Superalgebras [J]. J Algebra, 2000, 231(1): 1-38.
-
8徐丽媛,张庆成,孟道骥.低维Tortken超代数的分类与Tortken超代数的一些性质[J].数学物理学报（A辑）,2011,31(5):1190-1208. 被引量：2
-
9张庆成,张爽.广义Poisson超代数的同调与上同调群[J].数学年刊（A辑）,2011,32(3):257-266. 被引量：3
-
10贾志鹏,张庆成.李Color三系的幂零理想[J].吉林大学学报（理学版）,2011,49(4):674-678. 被引量：9
二级参考文献26
-
1Van Osdol D. Long exact sequences in the first variable for algebraic cohomology theories [J]. J Pure Appl Algebra, 1982, 23(3):271-309.
-
2Chevalley C, Eilenberg S. Cohomology theory of Lie groups and Lie algebras [J]. Trans Amer Math Soc, 1948, 63:85-124.
-
3Koszul J L. Homologie cohomologie des algebres de Lie [J]. Bull Soc Math France, 1950, 78:65-127.
-
4Hochschild G, Serre J. Cohomology of Lie algebras [J]. Ann Math, 1953, 57:591-603.
-
5Cartan H, Eilenberg S. Homological algebra [M]. Princeton: Princeton University Press, 1973.
-
6Leites D. Cohomology of Lie superalgebras [J]. Funct Anal Appl, 1975, 9:340-341.
-
7Fuks D, Leites D. Cohomology of Lie superalgebras [J]. C R Acad Bulg Sci, 1984, 37:1595-1596.
-
8Kac V. Lie superalgebras [J]. Adv Math, 1977, 26:8-96.
-
9Kac V. Classification of infinite-dimensional simple linearly compact Lie superalgebras [J]. Adv Math, 1998, 139:1-55.
-
10Scheunert M, Zhang R. Cohomology of Lie superalgebras and their generalizations [J]. Y Math Phys, 1998, 39:5024-5061.
共引文献10
-
1潘玉霞,张庆成,冯闪,王春月.二次李超三系的分解及唯一性[J].东北师大学报（自然科学版）,2012,44(2):9-13. 被引量：6
-
2王颂,张庆成,魏竹,王莹.李Poisson超代数的泛中心扩张[J].数学年刊（A辑）,2012,33(3):311-322.
-
3高秀娟,徐丽媛.Novikov Color代数与Tortken Color代数[J].吉林大学学报（理学版）,2016,54(2):197-201.
-
4张健,曹燕.李color三系的Frattini子系的性质[J].数学的实践与认识,2017,47(15):274-277. 被引量：1
-
5张健,曹燕.李Color三系的广义导子[J].吉林大学学报（理学版）,2017,55(6):1403-1406. 被引量：3
-
6张健,曹燕.李color三系的型心[J].黑龙江大学自然科学学报,2018,35(1):22-25. 被引量：2
-
7张健,曹燕.李color三系的导子、广义导子和拟导子[J].东北师大学报（自然科学版）,2018,50(3):13-16. 被引量：2
-
8曹燕.李Color三系的拟导子[J].吉林大学学报（理学版）,2019,57(4):849-852. 被引量：3
-
9张婉莹,曹燕.李color三系的上同调和Nijenhuis算子[J].数学杂志,2023,43(1):57-70.
-
10陈明露,曹燕.保积BiHom-Poisson Color代数的广义导子[J].吉林大学学报（理学版）,2023,61(4):724-732.
-
1王涵,那惠欣,张庆成.一类双色代数的构造[J].东北师大学报（自然科学版）,2016,48(2):1-5.
-
2La Mei YUAN,Sheng CHEN,Cai Xia HE.Hom-Gel'fand–Dorfman Super-bialgebras and Hom-Lie Conformal Superalgebras[J].Acta Mathematica Sinica,English Series,2017,33(1):96-116. 被引量：1
-
3乐茂华.关于Diophantine方程xn+1=2y2[J].云南师范大学学报（自然科学版）,2009,29(2):1-4.
-
4Li Sa,Qin Zhi.2-39 Manufacturing of Small Zirconia Kernels Using Improved Internal Gelation Process[J].IMP & HIRFL Annual Report,2014(1):79-79.
