Jacobian Conjecture via Differential Galois Theory

Symmetry Integrability and Geometry-Methods and Applications

article

Elżbieta Adamus¹  Teresa Crespo²  Zbigniew Hajto³ 

[1] Faculty of Applied Mathematics, AGH University of Science and Technology;Departament de Matemàtiques i Informàtica, Universitat de Barcelona;Faculty of Mathematics and Computer Science, Jagiellonian University

关键词: polynomial automorphisms;    Jacobian problem;    strongly normal extensions;   

DOI  :  10.3842/SIGMA.2019.034

来源: National Academy of Science of Ukraine

【 摘 要 】

We prove that a polynomial map is invertible if and only if some associated differential ring homomorphism is bijective. To this end, we use a theorem of Crespo and Hajto linking the invertibility of polynomial maps with Picard-Vessiot extensions of partial differential fields, the theory of strongly normal extensions as presented by Kovacic and the characterization of Picard-Vessiot extensions in terms of tensor products given by Levelt.

【 授权许可】

Unknown