A Bridge Between Lie Symmetries and Galois Groups
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.
KeywordsLie symmetries Symmetries of algebraic equations Galois group Galois representation of Lie symmetries
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