Let us define an associative algebra over $\mathbb{C}$ with generators $x, y, z$ and the following relations: $x^2=x, y^2=y, z^2=z, 2yxy=y, 3zyz=z, xz=zx$.
I am interested in finding center of this algebra or a large class of central elements (i.e. elements which commutes with all other elements in the algebra).
Also, is it possible to find/guess central elements of such algebras using computer packages like SAGE?