Druzkowski matrix search and D-nilpotent automorphisms

In 1939 Keller conjectured that any polynomial mapping f : C-n --> C-n with constant nonvanishing Jacobian determinant, should be invertible. This open problem bears the name of Jacobian conjecture. Druzkowski proved that cubic linens mappings are sufficient to decide the conjecture. For this important class we develop an algorithm that translates the constant-Jacobian condition into algebraic equations in the matrix of parameters. We also single out a natural special case ot these conditions, that we call D-nilpotency. The class of D-nilpotent matrices turns out to coincide with set of matrices that are permutation-similar to upper-triangular matrices. The corresponding cubic-linear maps are always invertible.