In differential geometry, the Schouten–Nijenhuis bracket, also known as the Schouten bracket, is a type of graded Lie bracket defined on multivector fields on a smooth manifold extending the Lie bracket of vector fields.
The Schouten-Nijenhuis bracket in differential geometry is a generalization of the Lie bracket to higher-order vector fields, building upon the concept of the Lie bracket for vector fields.