Star Product for Para-Grassmann Algebra of Order Two

In para-Grassmann algebra a noncommutative, associative star product $$*$$ (the Moyal product), which is a direct generalization of the star product in the algebra of Grassmann numbers is introduced. Isomorphism between the algebra of para-Grassmann numbers of order two equipped with the star product and the algebra of creation and annihilation operators $$a_{k}^{\pm }$$ obeying the para-Fermi statistics of the same order is established.