(mathematics) Any of the scalar products a_ij=2(r_i,r_j)/(r_i,r_i) that make up the Cartan matrix of a simple Lie algebra.

plural of Cartan integer

(mathematics) A certain kind of nilpotent subalgebra of a Lie algebra.

plural of Cartan subalgebra

Of or relating to Élie Cartan (1869–1951), influential French mathematician who did fundamental work in the theory of Lie groups and their geometric applications.