A smooth manifold G that is also a group such that multiplication (x, y) ↦ xy and inversion x ↦ x⁻¹ are smooth maps. Canonical examples: GL(n, ℝ), SO(n), SU(n), the Lorentz group. Continuous symmetries in physics are realised as…
Lie group
Related concepts
- Group (G, ·)
- Smooth manifold
- Ratner measure-rigidity theorems
- so(n) orthogonal Lie algebra: antisymmetric n×n matrices
- Noether's theorem (1918)
- Baker-Campbell-Hausdorff formula
- Kac-Moody algebra (affine extension)
- Flag variety / Borel-Weil
- PMNS / CKM unitarity as a Lie-group constraint (standard-model)
- Kolmogorov -5/3 law: E(k) = C_K * epsilon^{2/3} * k^{-5/3} via scaling-group dimensional analysis
- Nonlinear σ-model
- AdS/CFT (Maldacena 1997)
- Noether (1918)
- Wigner classification (1939)
- Eightfold way (Gell-Mann 1961)