Central Polynomials with Involution of $M_{1,1}(E)$

Let $K$ be an infinite field of characteristic $\neq 2$. In this article we study the $*$-space $C(R,*)$ of central polynomials with involution of the $K$-algebra $R= M_{1,1}(E)$, with an involution ($*$) obtanied from a superinvolution on $M_{1,1}(F)$ (i.e. $M_2(F)$ with its canonical $\mathbb{Z}_2$-grading).