Dixmier conjecture

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In algebra the Dixmier conjecture, first posed by Jacques Dixmier in 1968, is a conjecture about the endomorphisms of a Weyl algebra.

[edit] Statement

The Dixmier conjecture states that any endomorphism of a Weyl algebra is an automorphism.

It has been shown that the Dixmier conjecture is equivalent to the Jacobian conjecture.

[edit] References

• Dixmier, Jacques Sur les algèbres de Weyl. (French) Bull. Soc. Math. France 96 1968 209--242.
• Tsuchimoto, Yoshifumi. Endomorphisms of Weyl algebra and p-curvatures. Osaka J. Math. 42 (2005), 435-452.
• Belov-Kanel, Alexei; Kontsevich, Maxim. The Jacobian conjecture is stably equivalent to the Dixmier Conjecture. arXiv:math.RA/0512171