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Symmetry, Integrability and Geometry: Methods and Applications, 2019, Volume 15, 034, 7 pp.
DOI: https://doi.org/10.3842/SIGMA.2019.034 (Mi sigma1470) 		 
Jacobian Conjecture via Differential Galois Theory

Elżbieta Adamusa, Teresa Crespob, Zbigniew Hajtoc

a Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland
b Departament de Matemàtiques i Informàtica, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain
c Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Lojasiewicza 6, 30-348 Kraków, Poland
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DOI: https://doi.org/10.3842/SIGMA.2019.034
Abstract: 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.
Keywords: polynomial automorphisms, Jacobian problem, strongly normal extensions.
Funding agency Grant number
Ministerio de Economía y Competitividad de España MTM2015-66716-P
Ministry of Science and Higher Education (Poland)
This work was partially supported by the Faculty of Applied Mathematics AGH UST statutory tasks within subsidy of Ministry of Science and Higher Education. Crespo and Hajto acknowledge support by grant MTM2015-66716-P (MINECO/FEDER,UE).
Received: January 23, 2019; in final form May 1, 2019; Published online May 3, 2019
Bibliographic databases:
Document Type: Article
MSC: 14R10, 14R15, 13N15, 12F10
Language: English
Citation: Elżbieta Adamus, Teresa Crespo, Zbigniew Hajto, “Jacobian Conjecture via Differential Galois Theory”, SIGMA, 15 (2019), 034, 7 pp.
Citation in format AMSBIB
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\paper Jacobian Conjecture via Differential Galois Theory
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