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Moscow Mathematical Journal, 2007, Volume 7, Number 2, Pages 209–218
DOI: https://doi.org/10.17323/1609-4514-2007-7-2-209-218 (Mi mmj279) 		 
This article is cited in 66 scientific papers (total in 66 papers)

The Jacobian conjecture is stably equivalent to the Dixmier conjecture

A. Ya. Kanel-Belovab, M. L. Kontsevichc

a Moscow Institute of Open Education
b Hebrew University of Jerusalem
c Institut des Hautes Études Scientifiques
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DOI: https://doi.org/10.17323/1609-4514-2007-7-2-209-218
Abstract: The paper is devoted to the proof of equivalence of Jacobian and Dixmier conjectures. We show that $2n$-dimensional Jacobian conjecture implies Dixmier conjecture for $W_n$. The proof uses “antiquantization”: positive characteristics and Poisson brackets on the center of Weyl algebra in characteristic $p$.
Key words and phrases: Poisson brackets, symplectic structure, quantization, polynomial automorphism, Weyl algebra, differential operator, Jacobian conjecture.
Received: June 30, 2006
Bibliographic databases:
MSC: 16S32, 16S80, 14R15
Language: English
Citation: A. Ya. Kanel-Belov, M. L. Kontsevich, “The Jacobian conjecture is stably equivalent to the Dixmier conjecture”, Mosc. Math. J., 7:2 (2007), 209–218
Citation in format AMSBIB
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\by A.~Ya.~Kanel-Belov, M.~L.~Kontsevich
\paper The Jacobian conjecture is stably equivalent to the Dixmier conjecture
\jour Mosc. Math.~J.
\yr 2007
\vol 7
\issue 2
\pages 209--218
\mathnet{http://mi.mathnet.ru/mmj279}
\crossref{https://doi.org/10.17323/1609-4514-2007-7-2-209-218}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2337879}
\zmath{https://zbmath.org/?q=an:1128.16014}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000261829300004}
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