Cartan matrix

Let RE be a reduced root systemMathworldPlanetmath, with E a Euclidean vector space, with inner product (,), and let Π={α1,,αn} be a base of this root system. Then the Cartan matrixMathworldPlanetmathPlanetmath of the root system is the matrix


The Cartan matrix uniquely determines the root system, and is unique up to simultaneous permutationMathworldPlanetmath of the rows and columns. It is also the basis change matrix from the basis of fundamental weights to the basis of simple roots in E.

Title Cartan matrix
Canonical name CartanMatrix
Date of creation 2013-03-22 13:17:56
Last modified on 2013-03-22 13:17:56
Owner bwebste (988)
Last modified by bwebste (988)
Numerical id 4
Author bwebste (988)
Entry type Definition
Classification msc 17B20