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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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| รหัสดีโอไอ | |
| Creator | Nongkhran Sasom |
| Title | On finite-dimensional simple Poisson module on a certain Poisson algebra by using the specific Lie Structure method on Poisson maximal ideals |
| Contributor | Kanokporn Changton |
| Publisher | Faculty of Science, Ubon Ratchathani University |
| Publication Year | 2566 |
| Journal Title | Journal of Science and Science Education |
| Journal Vol. | 6 |
| Journal No. | 1 |
| Page no. | 40-49 |
| Keyword | Poisson algebras, Poisson ideal, Poisson maximal ideal, Derived algebra, Poisson modules |
| URL Website | https://so04.tci-thaijo.org/index.php/JSSE |
| Website title | Journal of Science and Science Education |
| ISSN | ISSN 2697-410X |
| Abstract | We study a Poisson algebra ????=?[????,????,????] with three generators and having three relations the same as the relations of ???? in Changtong et al. (2018). We classify the finite-dimensional simple Poisson modules over ???? by considering its Lie structure????/????????, where ???? is a Poisson maximal ideal of ????. We show that there are only five Poisson maximal ideals ????????, ????=????,????, . . . ,????. There are five ????-dimensional simple Poisson module annihilated by????????, ????=????,????, . . . ,????, for each positive integer ?????????. |
