Annihilation theorem and separation theorem for basic classical Lie superalgebras (Q2758959)
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scientific article; zbMATH DE number 1680619
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Annihilation theorem and separation theorem for basic classical Lie superalgebras |
scientific article; zbMATH DE number 1680619 |
Statements
10 December 2001
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Lie superalgebras
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universal enveloping algebras
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weights
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0.94607556
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0.92303467
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0.89237785
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0.8865162
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0.88646114
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0.8852272
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0.8807399
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Annihilation theorem and separation theorem for basic classical Lie superalgebras (English)
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Let \(\mathfrak g\) be a basic classical complex Lie superalgebra with a universal enveloping superalgebra \(U\). Denote by \(Z(\mathfrak g)\) the center of \(U\). In the author's previous paper [Ann. Inst. Fourier 50, 1745-1764 (2000; Zbl 1063.17006)], a special even element \(T\in Z(\mathfrak g)\) was constructed. A Verma module is strongly typical if \(T\) does not belong to its annihilator. The main result of the paper states that an annihilator of a strongly typical Verma module is a centrally generated ideal. Since each strongly typical Verma module is typical the author shows that for some classical Lie superalgebras the converse implication is valid.
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