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Dixmier conjecture

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

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

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

References

  1. 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)
  2. Tsuchimoto, Yoshifumi (2005), "Endomorphisms of Weyl algebra and p-curvatures", Osaka J. Math., 42: 435–452
  3. 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


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