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:
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)
“Mothers often are too easily intimidated by their children’s negative reactions...When the child cries or is unhappy, the mother reads this as meaning that she is a failure. This is why it is so important for a mother to know...that the process of growing up involves by definition things that her child is not going to like. Her job is not to create a bed of roses, but to help him learn how to pick his way through the thorns.”
—Elaine Heffner (20th century)
“The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
—Jean Baudrillard (b. 1929)