A Bridge Between Lie Symmetries and Galois Groups

  • Nail H. IbragimovEmail author
Part of the Abel Symposia book series (ABEL, volume 5)


A bridge between Lie symmetry groups for differential equations and Galois groups for algebraic equations is suggested. It is based on calculation of Lie symmetries for algebraic equations and their restriction of the roots of the equations under consideration. The approach is illustrated by several examples. An alternative representation of Lie symmetries, called the Galois representation, is provided for differential equations.


Lie symmetries Symmetries of algebraic equations Galois group Galois representation of Lie symmetries 


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  1. 1.
    N. H. Ibragimov, Primer of group analysis, Znanie, No. 8, Moscow, 1989, 44 p. (In Russian).Google Scholar
  2. 2.
    N. H.I bragimov, Elementary Lie group analysis and ordinary differential equations, Wiley, Chichester, 1999.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of Mathematics and Science, Research Centre ALGA: Advances in Lie GroupAnalysisBlekinge Institute of TechnologyKarlskronaSweden

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