Root vectors of the composition algebra of the Kronecker algebra

According to the canonical isomorphism between the positive part Uq⁺(g) of the Drinfeld–Jimbo quantum group Uq(g) and the generic composition algebra C(∆) of Λ, where the Kac–Moody Lie algebra g and the finite dimensional hereditary algebra Λ have the same diagram, in specially, we get a reali...

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Published in:Algebra and Discrete Mathematics
Date:2004
Main Author: Chen, X.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2004
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/155948
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Root vectors of the composition algebra of the Kronecker algebra / X. Chen // Algebra and Discrete Mathematics. — 2004. — Vol. 3, № 1. — С. 37–56. — Бібліогр.: 24 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-155948
record_format dspace
spelling Chen, X.
2019-06-17T15:46:33Z
2019-06-17T15:46:33Z
2004
Root vectors of the composition algebra of the Kronecker algebra / X. Chen // Algebra and Discrete Mathematics. — 2004. — Vol. 3, № 1. — С. 37–56. — Бібліогр.: 24 назв. — англ.
1726-3255
2000 Mathematics Subject Classification: 16G10, 17B37, 16G20, 81R50.
https://nasplib.isofts.kiev.ua/handle/123456789/155948
According to the canonical isomorphism between the positive part Uq⁺(g) of the Drinfeld–Jimbo quantum group Uq(g) and the generic composition algebra C(∆) of Λ, where the Kac–Moody Lie algebra g and the finite dimensional hereditary algebra Λ 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.
I would like to thank Professor V. Dlab and Professor E. Neher for their help and support. I am grateful to Professor C. M. Ringel and Professor J. Xiao for their helpful suggestions.
en
Інститут прикладної математики і механіки НАН України
Algebra and Discrete Mathematics
Root vectors of the composition algebra of the Kronecker algebra
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Root vectors of the composition algebra of the Kronecker algebra
spellingShingle Root vectors of the composition algebra of the Kronecker algebra
Chen, X.
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
author Chen, X.
author_facet Chen, X.
publishDate 2004
language English
container_title Algebra and Discrete Mathematics
publisher Інститут прикладної математики і механіки НАН України
format Article
description According to the canonical isomorphism between the positive part Uq⁺(g) of the Drinfeld–Jimbo quantum group Uq(g) and the generic composition algebra C(∆) of Λ, where the Kac–Moody Lie algebra g and the finite dimensional hereditary algebra Λ 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.
issn 1726-3255
url https://nasplib.isofts.kiev.ua/handle/123456789/155948
citation_txt Root vectors of the composition algebra of the Kronecker algebra / X. Chen // Algebra and Discrete Mathematics. — 2004. — Vol. 3, № 1. — С. 37–56. — Бібліогр.: 24 назв. — англ.
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first_indexed 2025-12-07T17:48:25Z
last_indexed 2025-12-07T17:48:25Z
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