Invariant tensors for simple groups |
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Authors: | JA de Azcárraga AJ Macfarlane AJ Mountain JC Pérez Bueno |
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Institution: | Department of Applied Mathematics and Theoretical Physics, Silver St., Cambridge CB3 9EW, UK |
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Abstract: | The forms of the invariant primitive tensors for the simple Lie algebras Al, Bl, Cl, and Dl are investigated. A new family of symmetric invariant tensors is introduced using the non-trivial cocycles for the Lie algebra cohomology. For the Al 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) are su(4) are also provided. Finally, new relations involving the d and f su(n) tensors are given. |
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