KillingCartan
KillingCartan is a term that refers to a specific type of geometrical object or concept arising from the study of Lie groups and Lie algebras. It is named after the mathematicians Elie Cartan and Wilhelm Killing, who made foundational contributions to these fields. The Killing form is a bilinear form defined on a Lie algebra. This form is invariant under the adjoint representation of the Lie algebra. In simpler terms, it's a way to measure how elements of the Lie algebra interact with each other in a way that respects the structure of the algebra.
The Killing form is a crucial tool in the classification of Lie algebras. Its properties, such as