Lie algebroid (Q2966)
From MaRDI portal
infinitesimal version of a Lie groupoid: manifold M with vector bundle E, vector bundle map ρ: E→TM, and a Lie bracket on sections of E, so that [s,ft] = (ρ(s)f)t+f[s,t] for any function f: M→ℝ and sections s, t of E
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Lie algebroid |
infinitesimal version of a Lie groupoid: manifold M with vector bundle E, vector bundle map ρ: E→TM, and a Lie bracket on sections of E, so that [s,ft] = (ρ(s)f)t+f[s,t] for any function f: M→ℝ and sections s, t of E |
Statements
![{\displaystyle \begin{aligned}\pi\colon E&\twoheadrightarrow M\\{}[,]\colon\Gamma(E)\otimes\Gamma(E)&\to\Gamma(E)\\\rho\colon E&\to\mathrm TM\\\forall e,e'\in\Gamma(E)\forall\phi\in\mathcal C^\infty(M)\colon[e,\phi e']&=(\rho(e)\phi) e' + \phi[e,e']\end{aligned}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/89ba565c2f0bfba6a507a0c2529699c7b3d2e343)
0 references
Identifiers
sh87001680
1 reference
Lie algebroid
0 references
LieAlgebroid
0 references
2776503324
0 references
/m/01t5gd
0 references
C2776503324
1 reference
987007541392405171
LieAlgebroids
0 references
Lie_algebroid
0 references
