Poisson Algebras II

Abstrac:

The concept of Poisson algebras is one of the most important concepts in mathematics that make a link between commutative and non-commutative algebra. Poisson algebras can be defined as Lie algebras that satisfy the Leibniz rule. Our research classifies some Poisson prime ideals of a certain class of Poisson algebras. The Poisson Algebras $A=K[t][x,y]$ are Poisson polynomial algebras in two variables $x$ and $y$ with coefficients on the Poisson polynomial algebra $K[t]$, where $K$ is an algebraically closed field of characteristic zero. There are three main classes of the class of the Poisson algebras $A$. We are interested in the Poisson spectrum of $A$, minimal and maximal Poisson ideals of $A$. The first class of Poisson algebras $A$ is presented in the poster “Poisson Algebras I”. This poster is shown the first part of the second class of Poisson algebras $A$.