Definition
Consider a Lie algebra g over a field K. Every element x of g defines the adjoint endomorphism ad(x) (also written as adx) of g with the help of the Lie bracket, as
- ad(x)(y) = .
Now, supposing g is of finite dimension, the trace of the composition of two such endomorphisms defines a symmetric bilinear form
- B(x, y) = trace(ad(x)ad(y)),
with values in K, the Killing form on g.
Read more about this topic: Killing Form
Famous quotes containing the word definition:
“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)
“Perhaps the best definition of progress would be the continuing efforts of men and women to narrow the gap between the convenience of the powers that be and the unwritten charter.”
—Nadine Gordimer (b. 1923)
“It is very hard to give a just definition of love. The most we can say of it is this: that in the soul, it is a desire to rule; in the spirit, it is a sympathy; and in the body, it is but a hidden and subtle desire to possess—after many mysteries—what one loves.”
—François, Duc De La Rochefoucauld (1613–1680)