93
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Galois Theory of Difference Equations with Periodic Parameters

, &
Pages 3902-3943 | Received 06 Aug 2012, Published online: 23 Apr 2014

REFERENCES

  • Amano , K. ( 2006 ). Liouville extensions of Artinian simple module algebras . Communications in Algebra 34 ( 5 ): 1811 – 1823 .
  • Amano , K. , Masuoka , A. ( 2005 ). Picard-Vessiot extensions of Artinian simple module algebras . Journal of Algebra 285 ( 2 ): 743 – 767 .
  • Amano , K. , Masuoka , A. , Takeuchi , M. ( 2009 ). Hopf algebraic approach to Picard-Vessiot theory . Handbook of Algebra 6 : 127 – 171 .
  • André , Y. ( 2001 ). Différentielles non commutatives et théorie de Galois différentielle ou aux différences . Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 34 ( 5 ): 685 – 739 .
  • Atiyah , M. , Macdonald , I. ( 1969 ). Introduction to Commutative Algebra . Reading , MA : Addison-Wesley .
  • Bourbaki , N. ( 1958 ). Algèbre. Chapitre 8: Modules et anneaux Semi-simples . Paris : Hermann .
  • Bourbaki , N. ( 1990 ). Algebra. Chapters 4–7. Springer .
  • Cassidy , P. ( 1972 ). Differential algebraic groups . American Journal of Mathematics 94 : 891 – 954 .
  • Cassidy , P. ( 1975 ). The differential rational representation algebra on a linear differential algebraic group . Journal of Algebra 37 ( 2 ): 223 – 238 .
  • Chatzidakis , Z. , Hardouin , C. , Singer , M. F. ( 2008 ). On the definitions of difference Galois groups. In: Model Theory with Applications to Algebra and Analysis. Vol. 1, 349. pp. 73–109 .
  • Cohn , R. M. ( 1965 ). Difference Algebra . New York-London-Sydney : Interscience Publishers John Wiley & Sons .
  • Di Vizio , L. ( 2012 ). Approche galoisienne de la transcendance différentielle. Journée annuelle 2012 de la SMF. URL http://divizio.perso.math.cnrs.fr/PREPRINTS/16-JourneeAnnuell eSMF/difftransc.pdf .
  • Di Vizio , L. , Hardouin , C. ( 2010 ). Courbures, groupes de Galois génériques et D-groupoïdes de Galois d'un système aux D-différences. C. R. Math. Acad. Sci. Paris 348(17–18):951–954. URL http://dx.doi.org/10.1016/j.crma.2010.08.001
  • Di Vizio , L. , Hardouin , C. ( 2011 ). Galois theories for q-difference equations: Comparison theorems. URL http://arxiv.org/abs/1002.4839
  • Di Vizio , L. , Hardouin , C. ( 2011 ). On the Grothendieck conjecture on p-curvatures for q-difference equations. URL http://arxiv.org/abs/1002.4839
  • Di Vizio , L. , Hardouin , C. ( 2011 ). Parameterized generic Galois groups for q-difference equations, followed by the appendix “The Galois D-groupoid of a q-difference system” by Anne Granier. URL http://arxiv.org/abs/1002.4839
  • Di Vizio , L. , Hardouin , C. ( 2012 ). Descent for differential Galois theory of difference equations. Confluence and q-dependency. Pacific Journal of Mathematics 256(1):79–104. URL http://dx.doi.org/10.2140/pjm.2012.256.79
  • Di Vizio , L. , Hardouin , C. , Wibmer , M. ( 2013 ). Difference Galois theory of linear differential equations. URL http://arxiv.org/abs/1302.7198
  • Granier , A. ( 2011 ). A Galois D-groupoid for q-difference equations . Annales de l'Institut Fourier 61 ( 4 ): 1493 – 1516 .
  • Hardouin , C. ( 2006 ). Hypertranscendance et groupes de Galois aux différences. URL http://arxiv.org/abs/math/0609646
  • Hardouin , C. ( 2008 ). Hypertranscendance des systèmes aux différences diagonaux. Compositio Mathematica 144(3):565–581. URL http://dx.doi.org/10.1112/S0010437X 07003430
  • Hardouin , C. , Singer , M. F. ( 2008 ). Differential Galois theory of linear difference equations. Mathematische Annalen 342(2):333–377. URL http://dx.doi.org/10.1007/ s00208-008-0238-z
  • Kamensky , M. (2013). Tannakian formalism over fields with operators. International Mathematics Research Notices 2013(24):5571–5622.
  • Lando , B. ( 1980 ). Extensions of difference specializations. Proceedings of the American Mathematical Society 79(2):197–202. URL http://dx.doi.org/10.1090/S0002-9939-1980-0565337-1
  • Levin , A. ( 2008 ). Difference algebra. Algebra and Applications. Vol. 8. New York: Springer. URL http://dx.doi.org/10.1007/978-1-4020-6947-5
  • Milne , J. ( 1980 ). Étale Cohomology . Princeton , NJ : Princeton University Press .
  • Morikawa , S. ( 2009 ). On a general difference Galois theory. I . Annales de l'Institut Fourier 59 ( 7 ): 2709 – 2732 .
  • Ovchinnikov , A. , Wibmer , M. ( 2013 ). σ-Galois theory of linear difference equations. http://arxiv.org/abs/1304.2649
  • van der Put , M. , Singer , M. F. ( 1997 ). Galois Theory of Difference Equations . Lecture Notes in Mathematics , Vol. 1666. Berlin : Springer-Verlag .
  • Rosen , E. ( 2008 ). A differential Chevalley theorem. URL http://arxiv.org/abs/ 0810.5486
  • Trushin , D. ( 2009 ). Difference Nullstellensatz. URL http://arxiv.org/abs/0908.3865
  • Trushin , D. ( 2009 ). Difference Nullstellensatz in the case of finite group. URL http:// arxiv.org/abs/0908.3863
  • Waterhouse , W. ( 1979 ). Introduction to Affine Group Schemes. New York: Springer. URL http://dx.doi.org/10.1007/978-1-4612-6217-6
  • Wibmer , M. ( 2010 ). Geometric Difference Galois Theory. Ph.D. thesis, University of Heidelberg .
  • Wibmer , M. ( 2012 ). A Chevalley theorem for difference equations. Mathematische Annalen 354(4):1369–1396. URL http://dx.doi.org/10.1007/s00208-011-0770-0
  • Communicated by K. Misra.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.