From Wikipedia, the free encyclopedia
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
-
^
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