On generation of the root lattice by roots

SIMON M. GOODWINa1

School of Mathematics, University of Birmingham, Birmingham, B15 2TT. e-mail: goodwin@maths.bham.ac.uk

Abstract

Let Φ be a root system and let Γ ⊆ Φ. In this short paper we prove that Γ contains a ${\mathbb Z}$-basis of the lattice that it generates.

(Received August 31 2005)

(Revised October 25 2005)