|
[Next][Prev] [Right] [Left] [Up] [Index] [Root]
A (real) reflection is an automorphism of a real vector space that acts as
negation on a one-dimensional subspace while fixing a hyperplane pointwise.
The subspace is described by a vector called the root,
while the hyperplane is described as the kernel
of an element of the dual space called the coroot.
A root system is a collection of root/coroot pairs that
is closed under the action of the corresponding reflections.
Only finite root systems are supported at the present time.
A root system gives a much more detailed description of a reflection
representation of a finite Coxeter group.
Root systems are used to classify the semisimple Lie algebras.
The closely related concept of a root datum is used to classify the
groups of Lie type.
This is described in Chapters ROOT SYSTEMS and ROOT DATA.
[Next][Prev] [Right] [Left] [Up] [Index] [Root]
|
