Journal of Lie Theory

no. 3
Local and Global Aspects of Lie Superposition Theorem
Journal of Lie Theory, Volume 20 (2010) no. 3, pp. 483-517
We give the global conditions for an ordinary differential equation to admit a superposition law of solutions in the classical sense. This completes the well-known Lie superposition theorem. We introduce rigorous notions of pretransitive Lie group action and Lie-Vessiot systems. We prove that an ordinary differential equation admit a superposition law if and only if its enveloping algebra is spanned by fundamental fields of a pretransitive Lie group action. We discuss the relationship of superposition laws with differential Galois theory and review the classical result of Lie.
DOI: 10.5802/jolt.606
Classification: 34M15, 35C05, 34M35, 34M45
Keywords: Non-linear superposition laws, Lie-Vessiot systems, Lie-Scheffers theorem, Galois theory of differential equations 
@article{JOLT_2010_20_3_a3,
     author = {D. Bl\'azquez-Sanz and J. J. Morales-Ruiz},
     title = {Local and {Global} {Aspects} of {Lie} {Superposition} {Theorem}},
     journal = {Journal of Lie Theory},
     pages = {483--517},
     year = {2010},
     volume = {20},
     number = {3},
     doi = {10.5802/jolt.606},
     zbl = {1205.34123},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.606/}
}
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D. Blázquez-Sanz; J. J. Morales-Ruiz. Local and Global Aspects of Lie Superposition Theorem. Journal of Lie Theory, Volume 20 (2010) no. 3, pp. 483-517. doi: 10.5802/jolt.606

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