Lie algebra and invariant tensor technology for \(g_2\) (Q2746657)
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scientific article; zbMATH DE number 1656367
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Lie algebra and invariant tensor technology for \(g_2\) |
scientific article; zbMATH DE number 1656367 |
Statements
23 June 2002
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Lie algebra \(g_2\)
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seven-dimensional representation
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invariant tensors
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Casimir operators
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Lie algebra and invariant tensor technology for \(g_2\) (English)
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Based on the fact that the exceptional Lie algebra \(g_2\), well known for instance in the physics of hadrons and nuclear spectroscopy, is a nonsymmetric subalgebra of \(so(7)\), which in turn is a symmetric subalgebra of \(su(7)\), the author explicitly constructs its seven-dimensional defining representation and the various \(g_2\) invariant tensors and discusses some identities, which include the trace and completeness properties of \(7 \times 7\) matrices, contraction relations, and the first- and second-class identities for the invariant tensors. The latter class provides useful information about the Casimir operators of \(g_2\).
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