simple root


vector spaceMathworldPlanetmath

Let RE be a root systemMathworldPlanetmath, with E a Euclidean vector space ( If R+ 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 E, and any positive root is a positive integer linear combinationMathworldPlanetmath 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 groupMathworldPlanetmathPlanetmath of the root system acts simply transitively on the set of bases.

Title simple root
Canonical name SimpleRoot
Date of creation 2013-03-22 13:11:49
Last modified on 2013-03-22 13:11:49
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 6
Author mathcam (2727)
Entry type Definition
Classification msc 17B20
Defines base