一类光滑泊松代数的构造
Construction of a Class of Smooth Poisson Algebras
DOI: 10.12677/pm.2026.1610215, PDF,   
作者: 李怡频, 刘立宇*:扬州大学数学学院,江苏 扬州
关键词: 泊松代数;光滑;典范丛;Poisson Algebra; Smooth; Canonical Bundle
摘要: 本文利用经典型广义外尔代数构造了一类泊松代数,证明了这类泊松代数是光滑代数且具有平凡的典范丛。
Abstract: A class of Poisson algebras are constructed via generalized Weyl algebra of classical type. It is showed that these Poisson algebras are smooth and have trivial canonical bundle.
文章引用:李怡频, 刘立宇. 一类光滑泊松代数的构造[J]. 理论数学, 2026, 16(10): 86-91. https://doi.org/10.12677/pm.2026.1610215

参考文献

[1] Crainic, M., Fernandes, R.L. and Mărcuț, I. (2021) Lectures on Poisson geometry. American Mathematical Society.
[2] 李克正. 交换代数与同调代数(第2版) [M]. 北京: 科学出版社, 2017.
[3] Luo, J., Wang, S.-Q. and Wu, Q.-S. (2024) Poincaré Duality for Smooth Poisson Algebras and BV Structure on Poisson Cohomology. Journal of Algebra, 649, 169-211.
https://doi.org/10.1016/j.jalgebra.2024.03.011
[4] Bavula, V. (1996) Tensor Homological Minimal Algebras, Global Dimension of the Tensor Product of Algebras and of Generalized Weyl algebras. Bulletin des Sciences Mathématiques, 120, 293-335.
[5] Liu, L. (2015) Homological Smoothness and Deformations of Generalized Weyl Algebras. Israel Journal of Mathematics, 209, 949-992.
https://doi.org/10.1007/s11856-015-1242-0
[6] Mukunda, N. and Sudarshan, E.C.G. (1976) Relation between Nambu and Hamiltonian Mechanics. Physical Review D, 13, 2846-2850.
https://doi.org/10.1103/physrevd.13.2846