The ${\rm Jacobian Conjecture}_{2n}$ implies the ${\rm Dixmier Problem}_n$
Abstract
Using the author's inversion formula for automorphisms of the Weyl algebras with polynomial coefficients and the bound on its degree a slightly shorter (algebraic) proof is given of the result of A. BelovKanel and M. Kontsevich that the Jacobian Conjecture implies the Dixmier Proplem. No originality is claimed.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 2005
 DOI:
 10.48550/arXiv.math/0512250
 arXiv:
 arXiv:math/0512250
 Bibcode:
 2005math.....12250B
 Keywords:

 Mathematics  Rings and Algebras;
 Mathematics  Commutative Algebra;
 Mathematics  Algebraic Geometry;
 14R15;
 14H37;
 16S32
 EPrint:
 3 pages