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…
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…