Invariant tensors for simple groups

Details Invariant tensors for simple groups Invariant tensors for simple groups

1997-06-03

arxiv.org/abs/physics/9706006v2

Nucl.Phys. B510 (1998) 657-687

Physics

Mathematical Physics

Latex file. 34 pages. (Trivial) misprints corrected. To appear in Nucl. Phys. B

Scientific paper

10.1016/S0550-3213(97)00609-3

The forms of the invariant primitive tensors for the simple Lie algebras A_l, B_l, C_l and D_l are investigated. A new family of symmetric invariant tensors is introduced using the non-trivial cocycles for the Lie algebra cohomology. For the A_l algebra it is explicitly shown that the generic forms of these tensors become zero except for the l primitive ones and that they give rise to the l primitive Casimir operators. Some recurrence and duality relations are given for the Lie algebra cocycles. Tables for the 3- and 5-cocycles for su(3) and su(4) are also provided. Finally, new relations involving the d and f su(n) tensors are given.

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