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)
“No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
—Florence Nightingale (1820–1910)
“It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.””
—Jane Adams (20th century)