Representations of \(\overline{\mathcal{U}}_{\mathfrak{q}} \mathrm{sl}(2 | 1)\) at even roots of unity (Q2795530)
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scientific article; zbMATH DE number 6559025
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Representations of \(\overline{\mathcal{U}}_{\mathfrak{q}} \mathrm{sl}(2 | 1)\) at even roots of unity |
scientific article; zbMATH DE number 6559025 |
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21 March 2016
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quantum group
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Nichols algebra
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representation
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Yetter-Drinfield module
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projective module
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Representations of \(\overline{\mathcal{U}}_{\mathfrak{q}} \mathrm{sl}(2 | 1)\) at even roots of unity (English)
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In this technical work the authors construct projective modules for the restricted quantum group \(\overline{\mathcal{U}}_q \mathrm{sl}(2|1)\) at even roots of unity.NEWLINENEWLINEIn Section II, the Hopf algebra \(\overline{\mathcal{U}}_q \mathrm{sl}(2|1)\) (also denoted \(U(X)\) ) is described in detail; in Section III, the equivalence between \(U(X)\)-modules and Yetter-Drinfield modules is investigated; Sections IV and V are devoted to simple and projective \(U(X)\)-modules respectively. Finally (as an application), the center of \(U(X)\) is constructed in Section VI.
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