Capelli elements for the algebra \(\mathfrak g_{2}\) (Q2844760)
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scientific article; zbMATH DE number 6199368
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Capelli elements for the algebra \(\mathfrak g_{2}\) |
scientific article; zbMATH DE number 6199368 |
Statements
19 August 2013
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central elements
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universal enveloping algebra
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Pfaffian
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0.8900792
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0.85255945
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0.8505558
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0.8467008
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0.8452734
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Capelli elements for the algebra \(\mathfrak g_{2}\) (English)
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The authors construct central elements (referred to as Capelli elements) in the universal enveloping algebra \(U({\mathfrak g}_2)\) of the simple Lie algebra \({\mathfrak g}_2\) in terms of sums of squares of Pfaffians of some matrices with entries belonging to \({\mathfrak g}_2\). A characterization of such elements in terms of vanishing properties is given and relations between them and higher Casimir elements are obtained.
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