dorsal/arxiv
View SchemaInvariant tensors and Casimir operators for simple compact Lie groups
| Authors | A. J. Mountain |
|---|---|
| Categories | |
| ArXiv ID | physics/9802012 |
| URL | https://arxiv.org/abs/physics/9802012 |
| DOI | 10.1063/1.532552 |
| Journal | J. Math. Phys. 39 (1998) 5601 |
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.
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"abstract": "The Casimir operators of a Lie algebra are in one-to-one correspondence with\nthe symmetric invariant tensors of the algebra. There is an infinite family of\nCasimir operators whose members are expressible in terms of a number of\nprimitive Casimirs equal to the rank of the underlying group. A systematic\nderivation is presented of a complete set of identities expressing\nnon-primitive symmetric tensors in terms of primitive tensors. Several examples\nare given including an application to an exceptional Lie algebra.",
"arxiv_id": "physics/9802012",
"authors": [
"A. J. Mountain"
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"doi": "10.1063/1.532552",
"journal_ref": "J. Math. Phys. 39 (1998) 5601",
"title": "Invariant tensors and Casimir operators for simple compact Lie groups",
"url": "https://arxiv.org/abs/physics/9802012"
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