**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) -

... In group theory and ring theory, square

**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)

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