Matrix Algebras with Involution and Central Polynomials

In this paper we study central polynomials for the matrix algebra M2n(K, *) with symplectic involution *. Their form is inspired by an apporach of Formanek and Bergman for investigating matrix identities by means of commutative algebra. We continue the investigations started earlier (1999, Bull. Austral. Math. Soc.60, 467–477 ; 2000, Comm. Algebra28, 4879–4887) by trying to give a complete form of the survey for n = 2, 3.