The symmetry algebra of a system of DEs is the Lie algebra of the symmetry group of a DE system. It is important to know if it is, or not, a solvable Lie algebra.
Given two Lie point symmetrys of an system of DEs, their Lie bracket is again a Lie point symmetry. In some cases it can be found a finite set of vector fields spanning, as a real vector space, the whole symmetry algebra. But in other cases the symmetry algebra is infinite-dimensional.
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Author of the notes: Antonio J. Pan-Collantes
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