Register to reply

Simple roots of a Lie Group from the full root system

Tags: root, roots, simple
Share this thread:
Mar16-10, 10:53 AM
P: 1
Hello all,

I'm attempting to find in literature a method of determining from a Lie algebra's full root system in an arbitrary basis which roots are simple. It seems there are many books, articles, etc on getting all the roots from the simple roots but none that go the other way.

My task is to take a system of positive roots and write an algorithm which builds the Dynkin diagram. I can identify the group quite easily, but building the Dynkin diagram is difficult. The algorithm I'm currently trying picks the first root and then looks for ones that have the correct dot products one at a time, thus building the diagram. However, it sometimes stops at smaller groups, identifying a D5 (SO(10)) group as D4 (SO(8)) or an E7 as an E6.

Is there any way other than using the Dynkin diagrams to identify a root as simple, or should I just start building linear combinations?

By the way, the basis for the roots is not specified, so I can't use the generic root structures for the groups presented in the literature.

Phys.Org News Partner Science news on
Experts defend operational earthquake forecasting, counter critiques
EU urged to convert TV frequencies to mobile broadband
Sierra Nevada freshwater runoff could drop 26 percent by 2100

Register to reply

Related Discussions
Symmetry group for roots Linear & Abstract Algebra 1
Building positive roots from simple roots Linear & Abstract Algebra 0
C10 Group, 10th roots unity with complex number multiplication Linear & Abstract Algebra 1
Root system? Linear & Abstract Algebra 0
What value of k gives no roots,one root, 2 roots? Introductory Physics Homework 14