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    188宝金博页面版: automorphisms of the weyl algebra

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    内容提示： arXiv:math/0512169v1 [math.RA] 8 Dec 2005Automorphisms of the Weyl algebraAlexei Belov-Kanel and Maxim KontsevichFebruary 2, 2008Abstract. We discuss a conjecture which says that the automorphism groupof the Weyl algebra in characteristic zero is canonically isomorphic to theautomorphism group of the corresponding Poisson algebra of classical poly-nomial symbols. Several arguments in favor of this conjecture are presented,all based on the consideration of the reduction of the Weyl algebra to positivechar...

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    arXiv:math/0512169v1 [math.RA] 8 Dec 2005Automorphisms of the Weyl algebraAlexei Belov-Kanel and Maxim KontsevichFebruary 2, 2008Abstract. We discuss a conjecture which says that the automorphism groupof the Weyl algebra in characteristic zero is canonically isomorphic to theautomorphism group of the corresponding Poisson algebra of classical poly-nomial symbols. Several arguments in favor of this conjecture are presented,all based on the consideration of the reduction of the Weyl algebra to positivecharacteristic.1IntroductionThis paper is devoted to the following surprising conjecture.Conjecture 1 The automorphism group of the Weyl algebra of index n overC is isomorphic to the group of the polynomial symplectomorphisms of a 2n-dimensional affine spaceAut(An,C) ? Aut(Pn,C) .Here for an integer n ≥ 1, denote by An,Cthe Weyl algebra of index nover CC?ˆ x1,..., ˆ x2n?/( relations [ˆ xi, ˆ xj] = ωij, 1 ≤ i,j ≤ 2n)where (ωij)1≤i,j≤2nis the standard skew-symmetric matrix:ωij= δi,n+j− δn+i,j,1

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