KnowraLie bracketLinked fromLinked fromThe 11 pages that link to Lie bracket, each with the reason it gives.All 11Broader topic 3Related 7Narrower topic 1Affine connectionRelated: The bracket appears in the connection's defining torsion expression.Jacobi identityRelated: The identity specifies how this operation must combine nested brackets.Adjoint representationRelated: The derivative of the adjoint action gives the bracket 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.