Invariant tensors and Casimir operators for simple compact Lie groups
Abstract
The Casimir operators of a Lie algebra are in one-to-one correspondence with the symmetric invariant tensors of the algebra. There is an infinite family of Casimir operators whose members are expressible in terms of a number of primitive Casimirs equal to the rank of the underlying group. A systematic derivation is presented of a complete set of identities expressing non-primitive symmetric tensors in terms of primitive tensors. Several examples are given including an application to an exceptional Lie algebra.
- Publication:
-
Journal of Mathematical Physics
- Pub Date:
- October 1998
- DOI:
- 10.1063/1.532552
- arXiv:
- arXiv:physics/9802012
- Bibcode:
- 1998JMP....39.5601M
- Keywords:
-
- 03.65.Fd;
- 02.20.Sv;
- 02.10.Sp;
- Algebraic methods;
- Lie algebras of Lie groups;
- Mathematical Physics;
- High Energy Physics - Theory
- E-Print:
- 11 pages, LaTeX, minor changes, version in J. Math. Phys