Coroot
From Wikipedia, the free encyclopedia
The structure and representation theory of a semisimple complex Lie algebra is characterised by its root system.
Given a root, α of a complex semisimple Lie algebra, there are associated to it two operators; Xα and Yα, the raising and lowering operators respectively. Their Lie bracket,
- Hα = [Xα,Yα]
is an element of the Cartan subalgebra. These operators are determined only up to scalar multipliers and it is often useful to set their lengths so as to form a subalgebra isomorphic to sl(2, C). Once this has been done H_{α} is called the coroot associated to α.
