Journal of Lanzhou University of Technology ›› 2020, Vol. 46 ›› Issue (5): 149-154.

• Scientific • Previous Articles     Next Articles

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

GAO Shou-lan1, WU Qi-wei1,2, ZHENG Shu-min1   

  1. 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

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

CLC Number: