Algebras of Jordan brackets and Generalized Poisson algebras

We construct a basis of free unital generalized Poisson superalgebras and a basis of free unital superalgebras of Jordan brackets. Also, we prove the analogue of Farkas’ Theorem for PI unital generalized Poisson algebras and PI unital algebras of Jordan brackets. Relations beetwen generic Poisson superalgebras and superalgebras of Jordan brackets will be studied.