I am trying to understand some of the definitions in Lie algebra/Lie groups.
So far I believe;
- A Cartan subalgebra is the largest possible set of elements that commute with each other in some representation. This would be made up of elements from the group.
- The generators of the group form the algebra of the group.
- Any operator that commutes with all the generators is described as a Casimir operator. The Casimir operators depend on the representation.
(Are any of these points wrong?)
I am wondering if there is some relationship between the Cartan sub algebra and the Casimir operators.