A Poincaré-Birkhoff-Witt theorem for the quantum group of type \(A_ n\) (Q1123252)
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scientific article; zbMATH DE number 4108965
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Poincaré-Birkhoff-Witt theorem for the quantum group of type \(A_ n\) |
scientific article; zbMATH DE number 4108965 |
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A Poincaré-Birkhoff-Witt theorem for the quantum group of type \(A_ n\) (English)
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1988
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The author describes a linear basis for the \(q\)-analogue \(U_ q(G)\) of the universal enveloping algebra in case \(G={\mathfrak sl}_{N+1}({\mathbb C})\). It follows, that \(U_ q({\mathfrak sl}_{N+1}({\mathbb C}))\) is a left (right) Noetherian ring without zero divisors provided \(q(q^ 8-1)\neq 0\).
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quantum groups
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\(q\)-deformation of enveloping algebras
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Hopf algebra
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explicit linear basis
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analogue of Poincaré-Birkhoff-Witt theorem
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triangular decomposition
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