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
1. Verfasser: Chen, Xueqing
Format: Artikel
Sprache:English
Veröffentlicht: Lugansk National Taras Shevchenko University 2018
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Online Zugang:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/979
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Algebra and Discrete Mathematics
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spelling 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
last_indexed 2024-04-12T06:27:33Z
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