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

Abstract

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