广义Jacobi恒等式与几何括号的刚性定理的证明  

Generalized Jacobi Identity and Proof of a Rigidity Theorem of Geometric Bracket

作　　者：王根 WANG Gen(School of Mathematics and Science,Xiamen University,Xiamen Fujian,361005)

机构地区：[1]厦门大学数学与科学学院,福建厦门361005

出　　处：《山西大同大学学报（自然科学版）》2023年第3期36-39,共4页Journal of Shanxi Datong University(Natural Science Edition)

摘　　要：为了研究与广义Poisson括号并列的几何括号的性质,以及与Jacobi恒等式的差异性,基于对广义结构Poisson括号的讨论,得到了在几何势函数为Casimir函数的条件下的广义Jacobi恒等式的具体表达式,证明了几何括号的一个普遍形式下的刚性定理以及一系列良好的推论。This paper studies the properties of geometric bracket juxtaposed with generalized Poisson bracket and the differences with Jacobi identities.Based on the discussion of generalized structural Poisson brackets,the specific expression of generalized Jacobi identities is obtained under the condition that the geometric potential function is Casimir function,and a rigidity theorem in the general form of geometric brackets and a series of positive corollaries are proven.

关 键 词：广义结构Poisson括号 广义Jacobi恒等式 几何势函数 刚性定理 几何括号 

分 类 号：O174.5[理学—数学]