A vector space 𝔤 with a bilinear bracket [·,·] that is anti-symmetric and satisfies the Jacobi identity. Tangent structure of Lie groups; classification of semisimple complex Lie algebras by Dynkin diagrams.
Lie algebra
Related concepts
- Vector space
- Jacobi identity
- Cartan-Killing classification
- Ring (R, +, ·)
- Moment map
- Poisson manifold
- SU(2) Lie algebra: T_a = σ_a/2, [T_a, T_b] = i·ε_abc·T_c
- Casimir invariant C_2 = Σ T^a T_a in centre of U(g)
- Jordan algebra (commutative nonassociative with Jordan identity)
- Alternative algebra (weakening of associativity: left/right alt)
- Flexible algebra and Malcev algebras (Jacobi generalisation)
- Local gauge invariance
- Gauge symmetry
- Lie algebra (physics)
- Gluon
- SU(2) CG: (½)⊗(½) = 1 ⊕ 0
- Pauli algebra: tr(σ_iσ_j) = 2δ_{ij}, [σ_i,σ_j] = 2iε_{ijk}σ_k
- Virasoro: [L_m,L_n] = (m−n)L_{m+n} + (c/12)m(m²−1)δ_{m+n,0}