Generalized Cartan matrix

Summary

A generalized Cartan matrix is a square integer matrix with $2$ on the diagonal and nonpositive entries off the diagonal. Its zero entries are placed symmetrically about the diagonal. It is the input data of a Kac–Moody algebra. The Cartan matrices of finite-dimensional semisimple Lie algebras are the generalized Cartan matrices of finite type. The matrices of affine type give the affine Lie algebras.