Some properties of generalized Cartan matrices
Part of the Progress in Mathematics book series (PM, volume 44)
In order to develop the theory of root systems of Kac-Moody algebras we need to know some properties of generalized Cartan matrices. It is convenient to work in a slightly more general situation. Unless otherwise stated, we will deal with a real n × n matrix A = (a ij ) which satisfies the following three properties:
A is indecomposable;
a ij ≤ 0 for i ≠ j;
a ij = 0 implies a ji = 0.
Unable to display preview. Download preview PDF.
Bibliographical notes and comments
© Springer Science+Business Media New York 1983