Dixmier conjecture
From HandWiki
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, http://www.numdam.org/item?id=BSMF_1968__96__209_0 (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, doi:10.17323/1609-4514-2007-7-2-209-218, Bibcode: 2005math.....12171B
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