Lie algebra classification for the Chazy equation and further topics related with this algebra.

Yeisson Alexis Acevedo-Agudelo; Danilo Andrés  García-Hernández; Oscar Mario  Londoño-Duque; Gabriel Ignacio  Loaiza-Ossa

doi:10.33571/rpolitec.v17n34a7

Authors

Yeisson Alexis Acevedo-Agudelo Magister en Matemáticas Aplicadas, Universidad EAFIT https://orcid.org/0000-0002-1640-9084
Danilo Andrés García-Hernández PhD en Matemáticas (IMECC), Universidade Estadual de Campinas https://orcid.org/0000-0002-0807-2602
Oscar Mario Londoño-Duque PhD en Matemáticas, Universidade Estadual de Campinas https://orcid.org/0000-0002-5666-8224
Gabriel Ignacio Loaiza-Ossa PhD en Ciencias Matemáticas, Universidad EAFIT https://orcid.org/0000-0003-2413-1139

DOI:

https://doi.org/10.33571/rpolitec.v17n34a7

Keywords:

Chazy equation, Lie symmetries, Classification of the group of Lie symmetries, Lie algebra, One parameter subgroup

Abstract

It is known that the classification of the Lie algebras is a classical problem. Due to Levi’s Theorem, the question can be reduced to the classification of semi-simple and solvable Lie algebras. This paper is devoted to classify the Lie algebra generated by the Lie symmetry group of the Chazy equation. We also present explicitly the one-parameter subgroup related to the infinitesimal generators of the Chazy symmetry group. Moreover, the classification of the Lie algebra associated with the optimal system is investigated.

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Author Biography

Yeisson Alexis Acevedo-Agudelo, Magister en Matemáticas Aplicadas, Universidad EAFIT

Magister en Matemáticas Aplicadas, Universidad EAFIT

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