- On finite-dimensional simple Poisson module on a certain Poisson algebra by using the specific Lie Structure method on Poisson maximal ideals -

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Published: Mar 19, 2023
DOI: https://doi.org/10.14456/jsse.2023.5
Keywords:
Poisson algebras, Poisson ideal, Poisson maximal ideal, Derived algebra, Poisson modules

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Nongkhran Sasom
Department of Mathematics Statistics and Computer, Faculty of Science, Ubon Ratchathani University
Kanokporn Changtong
Department of Mathematics Statistics and Computer, Faculty of Science, Ubon Ratchathani University

Abstract

We study a Poisson algebra A=C[x,y,z]  with three generators and having three relations the same as  the relations of  T  in Changtong et al. (2018). We classify the finite-dimensional simple Poisson modules over  A by considering its Lie structure J/J2  ,  where  J is a Poisson maximal ideal of A. We show that there are only five Poisson maximal ideals  Ji ,i=1,2,...,5. There are five d-dimensional  simple Poisson module annihilated by Ji,i=1,2,...,5, for each positive integer d>=1.

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How to Cite
Sasom, N., & Changtong, K. . (2023). - On finite-dimensional simple Poisson module on a certain Poisson algebra by using the specific Lie Structure method on Poisson maximal ideals: -. Journal of Science and Science Education (JSSE), 6(1), 40–49. https://doi.org/10.14456/jsse.2023.5
Issue
Vol. 6 No. 1 (2023): Vol. 6 No. 1: January - June 2023
Section
Research Articles in Science
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References

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