Killing Form - Definition

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:

    One definition of man is “an intelligence served by organs.”
    Ralph Waldo Emerson (1803–1882)

    According to our social pyramid, all men who feel displaced racially, culturally, and/or because of economic hardships will turn on those whom they feel they can order and humiliate, usually women, children, and animals—just as they have been ordered and humiliated by those privileged few who are in power. However, this definition does not explain why there are privileged men who behave this way toward women.
    Ana Castillo (b. 1953)

    ... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.
    George Eliot [Mary Ann (or Marian)