We check to see if some transformations of are Cartan involutions. Initialize the Lie algebra

Define a transformation and check that it is an involution.

Define a transformation It is a homomorphism, , but the symmetric bilinear form is not positive-definite.

The map is a homomorphism.

The map satisfies ,

The symmetric bilinear form is not positive-definite.

DifferentialGeometry, ApplyHomomorphism, ComposeTransformations, Killing, Query[Homomorphism], Transformation