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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| Дата: | 2018 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-9792018-05-14T08:03:48Z Root vectors of the composition algebra of the Kronecker algebra Chen, Xueqing Quantum group, root vector, Hall algebra, AR-quiver 16G10, 17B37, 16G20, 81R50 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. Lugansk National Taras Shevchenko University 2018-05-14 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/979 Algebra and Discrete Mathematics; Vol 3, No 1 (2004) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/979/508 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
Quantum group root vector Hall algebra AR-quiver 16G10 17B37 16G20 81R50 |
| spellingShingle |
Quantum group root vector Hall algebra AR-quiver 16G10 17B37 16G20 81R50 Chen, Xueqing Root vectors of the composition algebra of the Kronecker algebra |
| topic_facet |
Quantum group root vector Hall algebra AR-quiver 16G10 17B37 16G20 81R50 |
| format |
Article |
| author |
Chen, Xueqing |
| author_facet |
Chen, Xueqing |
| author_sort |
Chen, Xueqing |
| title |
Root vectors of the composition algebra of the Kronecker algebra |
| title_short |
Root vectors of the composition algebra of the Kronecker algebra |
| title_full |
Root vectors of the composition algebra of the Kronecker algebra |
| title_fullStr |
Root vectors of the composition algebra of the Kronecker algebra |
| title_full_unstemmed |
Root vectors of the composition algebra of the Kronecker algebra |
| title_sort |
root vectors of the composition algebra of the kronecker algebra |
| description |
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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/979 |
| work_keys_str_mv |
AT chenxueqing rootvectorsofthecompositionalgebraofthekroneckeralgebra |
| first_indexed |
2024-04-12T06:27:33Z |
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2024-04-12T06:27:33Z |
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1796109256812920832 |