# Dixmier conjecture

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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.

## References[edit]

**^**Dixmier, Jacques (1968), "Sur les algèbres de Weyl",*Bulletin de la Société Mathématique de France*,**96**: 209–242, doi:10.24033/bsmf.1667, MR 0242897 (problem 1)**^**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, Bibcode:2005math.....12171B, doi:10.17323/1609-4514-2007-7-2-209-218, MR 2337879, S2CID 15150838