A Central Polynomial of Low Degree for 4×4 Matrices Original Research Article

We have found a central polynomial of degree 13 for the 4 × 4 matrix algebra over a field of characteristic 0. This result agrees with the conjecture that the minimal degree of such polynomials for n × n matrices is (n2 + 3n − 2)/2. The polynomial has been obtained by explicitly exhibiting an essentially weak polynomial identity of degree 9 for 4 × 4 matrices.