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.

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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