Polynomial automorphisms, quantization and Jacobian conjecture related problems

2019/12/08 by Alexei Kanel-Belov, Kanel-Belov, Alexei, Andrey Elishev +8
Mathematics · Physics and Astronomy · #14R15 #14R20 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum chaos and dynamical systems #math.AG #msc:14R15 #msc:14R20

paper · pdf · doi:10.48550/arxiv.1912.03759

186 pages, no figures, v2: bibliography corrected. Review paper. Supported by the Russian Science Foundation grant No. 17-11-01377. arXiv admin note: substantial text overlap with arXiv:1308.0674, arXiv:1712.01490, arXiv:1901.01385, arXiv:1707.06450, arXiv:1207.2045, arXiv:1812.03307, arXiv:1808.04903

openalex publication_date 2019/12/08 · openalex created_date 2019/12/13 · arxiv created 2020/02/11 · arxiv updated 2020/02/12 · openalex updated_date 2026/07/28

Abstract

The purpose of this review paper is the collection, systematization and discussion of recent results concerning the quantization approach to the Jacobian conjecture, as well as certain related topics.

Citations

• The \rm Jacobian Conjecture_2n implies the \rm Dixmier Problem_n
• The invariant theory of n × n matrices
• Quantum mechanics as a statistical theory
• Independence of the B-KK Isomorphism of Infinite Prime
• Augmented Polynomial Symplectomorphisms and Quantization
• Quasi-identities on matrices and the Cayley-Hamilton polynomial
• An analogue of the Conjecture of Dixmier is true for the algebra of polynomial integro-differential operators
• The Jacobian Conjecture, together with Specht and Burnside-type problems
• Lifting of Polynomial Symplectomorphisms and Deformation Quantization
• On The Zariski Topology Of Automorphism Groups Of Affine Spaces And Algebras

Related

• Some Results On The Jacobian Conjecture And Polynomial Automorphisms
• Some arithmetic aspects of polynomial maps
• The Jacobian Conjecture, together with Specht and Burnside-type problems
• The Jacobian Conjecture, a Reduction of the Degree to the Quadratic Case
• An approach to the Jacobian Conjecture in terms of irreducibility