形变微分算子代数的Poisson代数结构  

The Poisson algebra structure of the deformed Lie algebra of differential operators

作　　者：高寿兰[1] 吴祺伟 郑姝敏 GAO Shou-lan;WU Qi-wei;ZHENG Shu-min(School of Science, Huzhou University, Huzhou 313000, China;Department of Mathematics, Shanghai University, Shanghai 200444, China)

机构地区：[1]湖州师范学院理学院,浙江湖州313000 [2]上海大学数学系,上海200444

出　　处：《兰州理工大学学报》2020年第5期149-154,共6页Journal of Lanzhou University of Technology

基　　金：国家自然科学基金(11871249,11971315)。

摘　　要：Poisson代数是指同时具有代数结构和李代数结构的一类代数,其代数结构和李代数结构满足Leibniz法则.利用Z-分次,通过Leibniz法则确定了形变微分算子代数L~的Poisson代数结构,说明了L~没有非平凡的结果Posson代数结构.Poisson algebras are the algebras having both an algebra structure and a Lie algebra structure together with the Leibniz law.By using the Z-grading the Poisson algebra structure on the deformed Lie algebra of differential operators L^is determined,through the Leibniz law,which shows the associative Poisson algebra structure on L^is trivial.

关 键 词：形变微分算子代数 POISSON代数 Leibniz法则 

分 类 号：O152.5[理学—数学]