Dixmier conjecture

In algebra the Dixmier conjecture, asked by Dixmier (1968, problem 1), is the conjecture that any endomorphism of a Weyl algebra is an automorphism.

Tsuchimoto (2005), and independently Belov-Kanel & Kontsevich (2007), showed that the Dixmier conjecture is stably equivalent to the Jacobian conjecture.

References

• Dixmier, Jacques (1968), "Sur les algèbres de Weyl", Bulletin de la Société Mathématique de France 96: 209–242, MR 0242897 
• Tsuchimoto, Yoshifumi (2005), "Endomorphisms of Weyl algebra and p-curvatures", Osaka J. Math. 42: 435–452 
• Belov-Kanel, Alexei; Kontsevich, Maxim (2007), "The Jacobian conjecture is stably equivalent to the Dixmier conjecture", Moscow Mathematical Journal 7 (2): 209–218, arXiv:math/0512171, MR 2337879