Jacobian Conjecture via Differential Galois Theory

被引：0

作者：

Adamus, Elzbieta ^{[1
]}

Crespo, Teresa ^{[2
]}

Hajto, Zbigniew ^{[3
]}

机构：

[1] AGH Univ Sci & Technol, Fac Appl Math, Al Mickiewicza 30, PL-30059 Krakow, Poland

[2] Univ Barcelona, Dept Matemat & Informat, Gran Via Corts Catalanes 585, E-08007 Barcelona, Spain

[3] Jagiellonian Univ, Fac Math & Comp Sci, Ul Lojasiewicza 6, PL-30348 Krakow, Poland

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2019年 / 15卷

关键词：

polynomial automorphisms; Jacobian problem; strongly normal extensions;

D O I：

10.3842/SIGMA.2019.034

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页数：7

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