LIE GROUPS ADMITTED BY AUTONOMOUS SYSTEM WITH GIVEN STRUCTURE CONSTANTS

This paper study the Lie groups admitted by differential equations. It is proved in this paper that for any n-th order autonomous system and any given structure constants Ckij, the system admits n-1 local one parameter Lie groups, and the non-trivial structure constants of the Lie module generated by infinitesimal generators of these Lie groups are just Ckij. This result shows that integrable system may admit unsolvable local Lie group.