guedes
Dec4-08, 07:12 AM
How can I know how many Casimirs does a Lie Algebra has?
Is there a theorem for this?
Or do we just have to form all possible "contractions" from the elements of the Lie algebra, and then commute it with all the elements of the algebra to check if it is zero? (with this example I'm thinking about the Lorentz or Poincaré group, where we just have P_{\mu} and M_{\mu\nu}, i.e, 10 elements in 4 dimensions. But what if we have a group with a 1000 elements?)
Is there a theorem for this?
Or do we just have to form all possible "contractions" from the elements of the Lie algebra, and then commute it with all the elements of the algebra to check if it is zero? (with this example I'm thinking about the Lorentz or Poincaré group, where we just have P_{\mu} and M_{\mu\nu}, i.e, 10 elements in 4 dimensions. But what if we have a group with a 1000 elements?)