Lie Bracket and Commutator
In group theory and ring theory, square brackets are used to denote the commutator. In group theory, the commutator is commonly defined as g−1h−1gh. In ring theory, the commutator is defined as ab − ba. Furthermore, in ring theory, braces are used to denote the anticommutator where {a,b} is defined as ab + ba.
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. There are many different forms of Lie bracket, in particular the Lie derivative and the Jacobi-Lie bracket.
Read more about this topic: Bracket (mathematics)
Famous quotes containing the word lie:
“The point is children lie to others for good and sufficient reasons, but they don’t kid themselves. They know who did what, but they feel no moral imperative to inform grownups.”
—Leontine Young (20th century)