KnowraJacobi identityLinked fromLinked fromThe 7 pages that link to Jacobi identity, each with the reason it gives.All 7Broader topic 2Related 5Lie algebraBroader topic: It constrains nested brackets and makes the bracket act like a commutator.Poisson bracketRelated: This identity is what makes Poisson brackets form a Lie algebra.Lie bracketRelated: This identity is the bracket's key consistency condition beyond bilinearity and alternation.Carl Gustav Jacob JacobiBroader topic: Named for Jacobi, it underlies Lie algebras and the Poisson bracket in mechanics.Lie's third theoremRelated: It is the algebraic consistency condition in the theorem's input.Baker–Campbell–Hausdorff formulaRelated: It governs relations among the nested brackets appearing in the series.Poincaré–Birkhoff–Witt theoremRelated: It ensures the bracket relations used to construct the enveloping algebra are consistent.