Lie Bracket

Lie Bracket Of Vector Fields - Examples
... For a Lie group, the Lie algebra is the tangent space at the identity, which can be identified with the left invariant vector fields ... The Lie bracket of the Lie algebra is then the Lie bracket of the left invariant vector fields, which is also left invariant ... For a matrix Lie group, smooth vector fields can be locally represented in the corresponding Lie algebra ...

Bracket (mathematics) - Lie Bracket and Commutator
... In group theory and ring theory, square brackets are used to denote the commutator ... The Lie bracket of a Lie algebra is a binary operation denoted by ... By using the commutator as a Lie bracket, every associative algebra can be turned into a Lie algebra ...

Lie Bracket Of Vector Fields - Definition
... The space of derivations of C∞(M) is a Lie algebra under the operation ... This Lie algebra structure can be transferred to the set of vector fields on M as follows ... The Jacobi–Lie bracket or simply Lie bracket, of two vector fields X and Y is the vector field such that Such a vector field exists because the ...