 
Summary: Extending systems to bases of root systems
Helmer ASLAKSEN
Department of Mathematics
National University of Singapore
Singapore 117543
Singapore
aslaksen@math.nus.edu.sg
www.math.nus.edu.sg/aslaksen/
Mong Lung LANG
Department of Mathematics
National University of Singapore
Singapore 117543
Singapore
matlml@math.nus.edu.sg
Abstract
Let R be an indecomposable root system. It is well known that any root
is part of a basis B of R. But when can you extend a set of two or more
roots to a basis B of R? A system is a linearly independent set of roots,
C, such that if and are in C, then is not a root. We will use
results of Dynkin and Bourbaki to show that with two exceptions, A3 Bn
