The _Jacobi identity_ is a property of some [bilinear maps](Bilinear%20map.md) which relates the order of operations of [linear maps](Linear%20map.md) to each other such that $[A,[B,C]] = [B,[C,A]] = [C,[A,B]] = 0.$ ^060f45 # The Jacobi identity in Lie algebras The Jacobi identity holds for all elements of $\mathfrak{g}$ where $\mathfrak{g}$ is a [Lie algebra.](Lie%20algebras.md) #MathematicalFoundations/Algebra/AbstractAlgebra/Algebras #MathematicalFoundations/Algebra/AbstractAlgebra/GroupTheory/Lie/LieGroups/Algebras/LieAlgebras #MathematicalFoundations/Algebra/AbstractAlgebra/LinearAlgebra/Operators/Matrices