Linked from

The 23 pages that link to Lie algebra, each with the reason it gives.

• Gauge theoryRelated: Gauge potentials and infinitesimal gauge transformations take values in this algebra.

• Lie groupBroader topic: It captures a Lie group’s infinitesimal structure at its identity.

• Élie CartanRelated: Cartan connected Lie groups to their infinitesimal algebras and classified the finite-dimensional simple cases.

• Poisson bracketRelated: Under the Poisson bracket, smooth functions acquire this algebraic structure.

• Yang–Mills theoryRelated: Its generators determine the gauge-field components and their interaction structure.

• Sophus LieBroader topic: This algebraic structure distilled the infinitesimal transformations Lie studied.

• Lie bracketBroader topic: A Lie bracket supplies the operation that makes its vector space a Lie algebra.

• Jacobi identityNarrower topic: The identity is one of the defining axioms of this algebraic structure.

• Adjoint representationNarrower topic: The adjoint representation acts on this vector space.

• Lie's third theoremNarrower topic: The theorem starts with this infinitesimal algebraic structure.

• Lorentz groupRelated: It captures the infinitesimal structure underlying continuous Lorentz transformations.

• Noncommutative algebraRelated: Its bracket extracts a noncommutative structure from associative multiplication.

• SU(2)Related: The Lie algebra su(2) captures infinitesimal transformations near the identity of SU(2).

• Baker–Campbell–Hausdorff formulaNarrower topic: The formula computes locally in this algebraic structure.

• Engel's theoremNarrower topic: Engel's theorem concerns Lie algebras represented by endomorphisms.

• Lie product formulaRelated: The formula relates exponentials of Lie algebra elements to products in a group.

• Lie's theoremNarrower topic: The theorem concerns representations of this algebraic structure.

• Poincaré–Birkhoff–Witt theoremNarrower topic: PBW applies to the Lie algebra whose generators and brackets define the enveloping algebra.

• Symmetry in quantum mechanicsRelated: Generators provide local descriptions of continuous symmetry transformations.

• Ado's theoremNarrower topic: Ado's theorem applies to every finite-dimensional Lie algebra.

• Algebra over a fieldBroader topic: Its multiplication-like bracket follows different laws from ordinary associative products.

• Closed-subgroup theoremNarrower topic: The subgroup’s tangent space at the identity becomes a Lie subalgebra.

• Coleman–Mandula theoremBroader topic: The theorem constrains how symmetry generators can combine and commute.