Let be a root system, with a Euclidean vector space (http://planetmath.org/VectorSpace). If is a set of positive roots, then a root is called simple if it is positive, and not the sum of any two positive roots. The simple roots form a basis of the vector space , and any positive root is a positive integer linear combination of simple roots.
A set of roots which is simple with respect to some choice of a set of positive roots is called a base. The Weyl group of the root system acts simply transitively on the set of bases.
|Date of creation||2013-03-22 13:11:49|
|Last modified on||2013-03-22 13:11:49|
|Last modified by||mathcam (2727)|