# Lie Bracket

Lie bracket can refer to:

• A bilinear binary operation (the commutator) defined on elements of a Lie algebra
• Lie bracket of vector fields

### Other articles related to "lie bracket, lie, brackets":

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 right hand side is a derivation of C∞(M), and the vector ...

### Famous quotes containing the word lie:

We laugh at him who steps out of his room at the very moment when the sun steps out, and says: “I will the sun to rise”; and at him who cannot stop the wheel, and says: “I will it to roll”; and at him who is taken down in a wrestling match, and says: “I lie here, but I will that I lie here!” And yet, all laughter aside, do we ever do anything other than one of these three things when we use the expression, “I will”?
Friedrich Nietzsche (1844–1900)