simple root
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.
Title | simple root |
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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 |