Simplicity of Lie algebras of Poisson brackets

Adel Alahmadi, Hamed Alsulami

Let $A$ be an associative commutative algebra with $1$ over a field of zero characteristic, $\{,\}:A\times A\to A$ is a Poisson bracket, $Z = \{ a \in A \mid \{a, A\} = (0) \}.…