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Mosc. Math. J., 2007, Volume 7, Number 2, Pages 209–218 (Mi mmj279)  

This article is cited in 34 scientific papers (total in 34 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

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.


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MSC: 16S32, 16S80, 14R15
Received: June 30, 2006

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
\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

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