形变微分算子代数的Poisson代数结构

兰州理工大学学报 ›› 2020, Vol. 46 ›› Issue (5): 149-154.

形变微分算子代数的Poisson代数结构

高寿兰¹, 吴祺伟^1,2, 郑姝敏¹

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

收稿日期:2019-09-11 出版日期:2020-10-28 发布日期:2020-11-06
作者简介:高寿兰(1978-),女,山东无棣人,博士,副教授.
基金资助:
国家自然科学基金(11871249,11971315)

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

GAO Shou-lan¹, WU Qi-wei^1,2, ZHENG Shu-min¹

1. School of Science, Huzhou University, Huzhou 313000, China;
2. Department of Mathematics, Shanghai University, Shanghai 200444, China

Received:2019-09-11 Online:2020-10-28 Published:2020-11-06

摘要/Abstract

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.

关键词: 形变微分算子代数, Poisson代数, Leibniz法则

Abstract: Poisson algebras are thealgebras having both an algebra structure and a Lie algebra structuretogether with the Leibniz law. By using the Z-gradingthe 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.

Key words: deformed Lie algebra of differential operators, Poisson algebra, Leibniz law

中图分类号:

O152.5

高寿兰, 吴祺伟, 郑姝敏. 形变微分算子代数的Poisson代数结构[J]. 兰州理工大学学报, 2020, 46(5): 149-154.

GAO Shou-lan, WU Qi-wei, ZHENG Shu-min. The Poisson algebra structure of the deformed Lie algebra of differential operators[J]. Journal of Lanzhou University of Technology, 2020, 46(5): 149-154.

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