Root vectors of the composition algebra of the Kronecker algebra
According to the canonical isomorphism between the positive part \({\bf U}^+_q({\bf g})\) of the Drinfeld-Jimbo quantum group \({\bf U} _q ({\bf g})\) and the generic composition algebra \({\mathcal C} (\Delta)\) of \(\Lambda\), where the Kac-Moody Lie algebra \({\bf g}\) and the finite dimensional...
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| Datum: | 2018 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2018
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| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/979 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Zusammenfassung: | According to the canonical isomorphism between the positive part \({\bf U}^+_q({\bf g})\) of the Drinfeld-Jimbo quantum group \({\bf U} _q ({\bf g})\) and the generic composition algebra \({\mathcal C} (\Delta)\) of \(\Lambda\), where the Kac-Moody Lie algebra \({\bf g}\) and the finite dimensional hereditary algebra \(\Lambda\) have the same diagram, in specially, we get a realization of quantum root vectors of the generic composition algebra of the Kronecker algebra by using the Ringel-Hall approach. The commutation relations among all root vectors are given and an integral PBW-basis of this algebra is also obtained. |
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