A central polynomial of low degree for \(4\times 4\) matrices (Q1335080)

The main result of this paper is that the authors determine a central polynomial for \(4\times 4\) matrices of degree 13. This result agrees with the conjecture that the minimal degree of such polynomials for \(n\times n\) matrices is \((n^2+3n-2)/2\). The polynomial has been obtained by explicitly exhibiting an essentially weak polynomial identity of degree 9 for \(4\times 4\) matrices. The paper contains sections of The Weak Polynomial Identity and from Weak Polynomial Identities to Central Polynomials following Introduction and Preliminaries.