Gröbner-Shirshov bases for quantum enveloping algebras (Q677449)
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scientific article; zbMATH DE number 997616
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Gröbner-Shirshov bases for quantum enveloping algebras |
scientific article; zbMATH DE number 997616 |
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Gröbner-Shirshov bases for quantum enveloping algebras (English)
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2 February 1999
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The authors give a method for finding Gröbner-Shirshov bases for the quantum algebras of \textit{V. G. Drinfel'd} [Sov. Math., Dokl. 32, 256-258 (1985); translation from Dokl. Akad. Nauk SSSR 283, No. 5, 1060-1064 (1985; Zbl 0588.17015)] and \textit{M. Jimbo} [Lett. Math. Phys. 10, No. 1, 63-69 (1985; Zbl 0587.17004)]. It is shown how the methods can be applied to Kac-Moody algebras. They explicitly find the bases for quantum enveloping algebras of type \(A_N\) (for \(q^8\neq 1\)).
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Gröbner-Shirshov basis
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quantum enveloping algebra
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Kac-Moody algebra
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