广义几何Lie代数及其研究  

Generalized geometric Lie algebra and its research

作　　者：王根 梁玉霞 WANG Gen;LIANG Yuxia(Department of Mathematics,Xiamen University,Xiamen 361005,Fujian,China;School of Mathematics and Science,Tianjin Normal University,Tianjin 300387,China)

机构地区：[1]厦门大学数学与科学学院,福建厦门361005 [2]天津师范大学数学科学学院,天津300387

出　　处：《上海师范大学学报（自然科学版）》2023年第3期327-331,共5页Journal of Shanghai Normal University(Natural Sciences)

摘　　要：为了探究Lie代数的一般拓展意义,构造了一般广义几何Lie括号与广义几何Lie代数,使得Lie代数是其一种特殊情况;然后讨论了它们的相关性质,证明了流形上向量场在广义几何Lie括号下的微分同胚,改进了Lie括号给出的结果。In order to explore the general extension meanings of Lie algebra,the generalized geometric Lie bracket and generalized geometric Lie algebra are constructed and their related properties are studied,containing Lie algebra as a special case.The differential homeomorphism of vector field on manifolds under generalized geometric Lie bracket is proved,and the result given by Lie bracket is improved.

关 键 词：LIE代数 广义几何Lie括号 微分同胚 Lie括号 向量场 

分 类 号：O174.5[理学—数学]