多项式Poisson代数上的有限维单Poisson模

Simple Poisson modules over some polynomial Poisson algebras

为了探究一类Poisson代数A上的有限维单Poisson模的同构类,通过计算A上的Poisson极大理想,采用分类讨论思想,得到对任意的正整数d,Poisson代数A上有5个d-维单Poisson模的同构类.

It was aimed to study the simple Poisson modules over Poisson algebra A.By caculating the Poisson maximal ideal of A and based on the idea of classification discussion,it was proved that there existed five d -dimensional simple Poisson modules over Poisson algebra A for any positive integer d ≥1.