Poisson primitive ideals of a Poisson order

Abstract

Let R be an affine Poisson algebra over a field of characteristic zero and let A be a Poisson order over R. It is proved that every Poisson primitive ideal of A is annihilator of a simple Poisson A-module.

Keywords:

• Poisson algebra
• Poisson enveloping algebra
• Poisson order
• Poisson primitive ideal

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 17B63
• 16S35

Additional information

Funding

The second author is supported by National Research Foundation of Korea, NRF-2020R1A2C1A01004133. The third author is supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education (NRF-2019R1A6A3A01093778).