Polynomial automorphisms, quantization and Jacobian conjecture related problems

2019/12/08 by Alexei Kanel-Belov, Andrey Elishev, Kanel-Belov, Alexei +7
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

paper · pdf · doi:10.48550/arxiv.1912.03759

openalex publication_date 2019/12/08 · openalex created_date 2019/12/13 · 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

Related

• Some Results On The Jacobian Conjecture And Polynomial Automorphisms
• Some arithmetic aspects of polynomial maps
• An approach to the Jacobian Conjecture in terms of irreducibility
• An effective approach to Picard-Vessiot theory and the Jacobian Conjecture
• On mappings with Jacobian one