Given a partial differential equation, after computing the Lie point symmetries of this PDE, means a one-parameter group (Lie group) of transformation that leaves the set of solutions of the PDE invariant using Lie's theorem (infinitesimal criterion of symmetry), this one parameter group is generated by a vector field (infinitesimal symmetry) see Olver's book application of Lie groups to differential equations, but he does not prove my following question. While computing these vector fields, I want to prove that they form a Lie algebra.
2026-03-28 14:44:08.1774709048
Why or how to prove that the infinitesimal symmetries of a differential equation form a Lie algebra?
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