simple root
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vector space
Let be a root system, with a Euclidean vector space (http://planetmath.org/VectorSpace). If is a set ofpositive roots, then a root is called simple if it is positive, and not the sum of any twopositive roots. The simple roots form a basis of the vector space , and any positive rootis 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 abase. The Weyl group of the root system acts simply transitively on the set of bases.