# generalized Cartan matrix

A generalized Cartan matrix is a matrix $A$ whose diagonal entries are all 2, and whose off-diagonal entries are nonpositive integers, such that $a_{ij}=0$ if and only if $a_{ji}=0$. Such a matrix is called symmetrizable if there is a diagonal matrix $B$ such that $AB$ is symmetric.

Title generalized Cartan matrix GeneralizedCartanMatrix 2013-03-22 13:52:56 2013-03-22 13:52:56 bwebste (988) bwebste (988) 5 bwebste (988) Definition msc 17B67 ExtendedCartanMatrix symmetrizable