Dixmier conjecture

Not to be confused with the Dixmier Problem in representation theory.

In algebra the Dixmier conjecture, asked by Jacques Dixmier in 1968,^[1] is the conjecture that any endomorphism of a Weyl algebra is an automorphism.

Tsuchimoto in 2005,^[2] and independently Belov-Kanel and Kontsevich in 2007,^[3] showed that the Dixmier conjecture is stably equivalent to the Jacobian conjecture.