**Lie bracket of vector fields - Wikipedia**
https://en.wikipedia.org/wiki/Lie_bracket_of_vector_fields

In the mathematical field of differential topology, the Lie bracket of vector fields, also known as the Jacobi–Lie bracket or the commutator of vector fields, is an operator that assigns to any two vector fields X and Y on a smooth manifold M a third vector field denoted [X, Y].. Conceptually, the Lie bracket [X, Y] is the derivative of Y along the flow generated by X, and is sometimes ...

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