  Poisson algebra is usually defined to be a commutative algebra together with
a Lie bracket, and these operations are required to satisfy the Leibniz rule.
We describe Poisson structures in terms of a single bilinear operation. This
enables us to explore Poisson algebras in the realm of non-associative
algebras. We study their algebraic and cohomological properties, their
deformations as non-associative algebras, and give a classification in low
dimensions
