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 plays a crucial role in differential geometry as a means to generalize the concept of the Lie bracket from vector fields to higher-order multivector fields on smooth manifolds.