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arXiv:2410.06959math.RA

The Conjecture of Dixmier for the first Weyl algebra is true

Alexander Zheglov

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Abstract

Let $K$ be a field of characteristic zero, let $A_1=K[x][\partial ]$ be the first Weyl algebra. In this paper we prove that the Dixmier conjecture for the first Weyl algebra is true, i.e. each algebra endomorphism of the algebra $A_1$ is an automorphism.

arXiv comments
25 p; v2: minor changes; V3: improved exposition, more details to the proof added, 34 p; V4: significantly improved version: investigation of solutions to the string equation is added, 67 p; V5: extended introduction, more comments and references added, calculations at the last stage of the proof are simplified, some typos fixed, 78 p
Journal reference
DOI
Subjects
math.RARings and Algebras math-phMathematical Physics math.AGAlgebraic Geometry math.QAQuantum Algebra

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  1. Claude Fable produced a counterexample to the Jacobian Conjecture 1 comment

    • Wasn't it proven true in general for n=2 (NGL I wanted to suggest someone to go for the JC using 5.6 after the CDC proof came out, but then on reflection felt I should neither waste people's time NOR contribute to the myth of AI :) My prediction is that the bubble will burst in…

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