Linked from

The 39 pages that link to Lie group, each with the reason it gives.

• Differential geometryRelated: Its smooth structure makes continuous symmetries accessible to geometric methods.

• Gauge theoryNarrower topic: Its elements specify the continuous transformations allowed by a gauge theory.

• Group theoryBroader topic: Lie groups model continuous symmetries in geometry and physics.

• GroupBroader topic: Continuous symmetries in geometry and physics are often described by Lie groups.

• Tangent spaceRelated: Its identity tangent space encodes the Lie algebra and local group structure.

• Élie CartanNarrower topic: Cartan’s classification and representation work made Lie groups a central subject of modern mathematics.

• Felix KleinRelated: Continuous symmetry groups connect Klein’s geometric viewpoint to modern geometry and physics.

• Lie algebraRelated: Its tangent space at the identity carries a natural Lie algebra.

• Smooth manifoldRelated: Lie groups combine manifold calculus with continuous symmetry.

• Hermann WeylNarrower topic: Lie groups gave Weyl a language for continuous symmetries in geometry and physics.

• ManifoldRelated: Lie groups combine manifold geometry with algebraic symmetry.

• Symmetry groupRelated: Continuous symmetry groups in geometry and physics are commonly Lie groups.

• Yang–Mills theoryNarrower topic: Yang–Mills gauge symmetries are built from continuous groups.

• Sophus LieBroader topic: Lie’s transformation groups became the modern framework for continuous symmetries.

• Irreducible representationRelated: Its continuous symmetries have rich families of irreducible representations.

• Lie bracketRelated: Its tangent space at the identity carries a Lie bracket encoding infinitesimal group structure.

• Spherical symmetryNarrower topic: Continuous rotation symmetries are described using this mathematical framework.

• Jacobi identityRelated: The tangent space at its identity forms a Lie algebra whose bracket satisfies Jacobi.

• Erlangen programRelated: Continuous transformation groups provide the natural algebraic setting for many geometries.

• Geometric group theoryCompared with: Lie groups carry continuous geometry intrinsically, unlike discrete groups studied through external spaces.

• Lie's third theoremNarrower topic: The theorem identifies the global object integrating the given Lie algebra.

• Lorentz groupRelated: The Lorentz group is continuous and has a smooth local structure.

• SU(2)Narrower topic: SU(2) is a compact Lie group, so its algebraic and continuous structures interact.

• Baker–Campbell–Hausdorff formulaNarrower topic: Its local multiplication is what the formula translates into Lie-algebra terms.

• Yang–Mills existence and mass gapRelated: The choice of a compact simple gauge group specifies the theory in the problem.

• Differentiable manifoldBroader topic: Its smooth structure makes continuous symmetries accessible to differential calculus.

• Lie product formulaNarrower topic: Exponentials of Lie algebra elements describe local motion within these groups.

• Poincaré–Birkhoff–Witt theoremNarrower topic: The theorem developed from algebraic questions arising in the study of Lie groups.

• Symmetry in quantum mechanicsRelated: Continuous quantum symmetries, such as rotations, are modeled by Lie groups.

• Ado's theoremRelated: Finite-dimensional Lie algebra representations connect to linear actions of Lie groups.

• Mostow rigidity theoremNarrower topic: Hyperbolic isometries form a Lie group, central to rigidity arguments.

• Weyl character formulaRelated: The formula applies to finite-dimensional representations of semisimple Lie groups as well as Lie algebras.

• Closed-subgroup theoremNarrower topic: The theorem emerged from the structural study of these groups.

• Grigory MargulisNarrower topic: Continuous symmetries in Lie groups underpin many of the groups Margulis studied.

• Hilbert–Smith conjectureCompared with: The conjecture predicts that every effective locally compact symmetry group has this structure.

• Masahiro SakuraiRelated: Continuous symmetry groups provide mathematical tools for the particle theories Sakurai studied.

• Mathematical formulation of the Standard ModelRelated: The Standard Model’s gauge symmetries are organized by Lie groups.

• Rotations in 4-dimensional Euclidean spaceRelated: SO(4) is a six-dimensional Lie group, enabling calculus on families of rotations.

• Symmetry-based models (mathematical physics)Broader topic: Continuous symmetries such as rotations and translations are commonly represented by Lie groups.