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Relative D-groups and differential Galois theory in several derivations


Author: Omar León Sánchez
Journal: Trans. Amer. Math. Soc. 367 (2015), 7613-7638
MSC (2010): Primary 03C60, 12H05
DOI: https://doi.org/10.1090/S0002-9947-2015-06249-7
Published electronically: March 13, 2015
MathSciNet review: 3391895
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Abstract: The Galois theory of logarithmic differential equations with respect to relative D-groups in partial differential-algebraic geometry is developed. This theory generalizes simultaneusly the parametrized Picard-Vessiot theory of Cassidy and Singer and the finite-dimensional theory of Pillay's generalized strongly normal extensions.


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Additional Information

Omar León Sánchez
Affiliation: Department of Mathematics, University of Waterloo, West Waterloo, Ontario N2L 3G1, Canada
Address at time of publication: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4L8, Canada
Email: oleonsan@math.mcmaster.ca

DOI: https://doi.org/10.1090/S0002-9947-2015-06249-7
Keywords: Differential Galois theory, D-groups, model theory
Received by editor(s): December 1, 2012
Received by editor(s) in revised form: July 19, 2013
Published electronically: March 13, 2015
Article copyright: © Copyright 2015 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.