root system
A root system is a key notion in the classification and the representation theory of reflection groups and of semi-simple Lie algebras. Let be a Euclidean vector space with inner product . A root system is a finite spanning set such that for every , the orthogonal reflection
A root system is called crystallographic if is an integer for all .
A root system is called reduced if for all , we have for only.
We call a root system indecomposable if there is no proper decomposition such that every vector in is orthogonal to every vector in .
Title | root system |
Canonical name | RootSystem |
Date of creation | 2013-03-22 13:11:30 |
Last modified on | 2013-03-22 13:11:30 |
Owner | rmilson (146) |
Last modified by | rmilson (146) |
Numerical id | 13 |
Author | rmilson (146) |
Entry type | Definition |
Classification | msc 17B20 |
Related topic | SimpleAndSemiSimpleLieAlgebras2 |
Related topic | LieAlgebra |
Defines | reduced root system |
Defines | root |
Defines | root space |
Defines | root decomposition |
Defines | indecomposable |
Defines | reduced |
Defines | crystallographic |