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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 fieldsX{\displaystyle X} and Y{\displaystyle Y} on a smooth manifoldM{\displaystyle M} a third vector field denoted [X,Y]{\displaystyle [X,Y]}.

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