THE JOURNAL OF APPLIED SCIENCE

Volume 21, No. 01, Month JANUARY, Year 2022, Pages 244 - 580

Finite dimensional simple poisson modules of a poisson algebras a

Nagornchat Chansuriya, Supaporn Fongchanta

Abstract Download PDF

This study focus on a Poisson algebra A = x, y, z with a Poisson bracket x, y = yx + z, y, z = zy + x, z, x = xz + y. There are precisely five Poisson maximal ideals as following. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 2 3 4 5 , 1 1 1 , 1 1 1 , 1 1 1 , 1 1 1 . J xA yA zA J x A y A z A J x A y A z A J x A y A z A J x A y A z A = + + = + + + + + = + + − + − = − + + + − = − + − + + In this research, we determine the finite dimensional simple Poisson modules annihilated by ; 1,2, ,5 i J i= .

Keywords

Poisson algebra, Poisson module, simple Poisson module, finite-demensional simple Poisson module

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