Linked from

The 11 pages that link to Lie bracket, each with the reason it gives.

• Lie algebraBroader topic: This operation supplies the algebra’s defining interaction between elements.

• Affine connectionRelated: The bracket appears in the connection's defining torsion expression.

• Sophus LieBroader topic: Brackets capture how the infinitesimal transformations combine.

• Jacobi identityRelated: The identity specifies how this operation must combine nested brackets.

• Adjoint representationRelated: The derivative of the adjoint action gives the bracket operation.

• Lie's third theoremBroader topic: The bracket is the algebraic data that the resulting group's tangent structure must preserve.

• Baker–Campbell–Hausdorff formulaNarrower topic: The formula’s correction terms are built from this operation.

• Flow (mathematics)Related: It reveals when composing two flows in opposite orders produces different transformations.

• Engel's theoremRelated: For endomorphisms, the bracket is the commutator that defines the algebra's structure.

• Poincaré–Birkhoff–Witt theoremRelated: The relations identifying commutators with brackets are precisely the quotient relations used in PBW.

• Fundamental theorem of Riemannian geometryRelated: It appears in the Koszul formula and encodes the torsion-free condition.