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

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.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 parame-ter subgroup related to the infinitesimal generators of the Chazy symmetry group. Moreover the classification of the Lie algebra associated to the optimal system is investigated. La clasificación de las álgebras de Lie es un problema clásico. Acorde al teorema de Levi la cuestión puede reducirse a la clasificación de álgebras de Lie semi-simples y solubles. Este artículo está dedicado a clasificar el álgebra de Lie generada por el grupo de simetría de Lie para la ecuación de Chazy. También presentamos explícitamente los subgrupos a un parámetro  relacionados con los generadores de las simetrías del grupo de Chazy. Además, la clasificación de la álgebra de Lie asociada al sistema optimo es investigada