mathematics, the term Cartan matrix has three meanings. All of these are named after the French mathematician Élie Cartan. Amusingly, the Cartan matrices in the...

to the eight nodes in the Dynkin diagram in the order chosen for the Cartan matrix below, i.e., the nodes are read in the seven-node chain first, with...

character formula, Cartan subalgebra, roots, weights, and so on. A symmetrized Cartan matrix is a (possibly infinite) square matrix with entries c i j...

that is simply connected. The Dynkin diagram for G2 is given by . Its Cartan matrix is: [ 2 − 3 − 1 2 ] {\displaystyle \left[{\begin{array}{rr}2&-3\\-1...

transpose of D with D itself results in the Cartan matrix, usually denoted C; this is a symmetric matrix such that the entries in its j-th row are the...

that can be defined by generators and relations through a generalized Cartan matrix. These algebras form a generalization of finite-dimensional semisimple...

the result of substituting the matrix itself into its own characteristic polynomial yields the zero matrix. Cartan matrix Brown 1991, Definition I.2.28...

In mathematics, SO(8) is the special orthogonal group acting on eight-dimensional Euclidean space. It could be either a real or complex simple Lie group...

The designation E6 comes from the Cartan–Killing classification of the complex simple Lie algebras (see Élie Cartan § Work). This classifies Lie algebras...

choice of simple roots for F4, , is given by the rows of the following matrix: [ 0 1 − 1 0 0 0 1 − 1 0 0 0 1 1 2 − 1 2 − 1 2 − 1 2 ] {\displaystyle...