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 |
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| Date: | 2004 |
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| Language: | English |
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Інститут прикладної математики і механіки НАН України
2004
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/155948 |
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| 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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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 |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| 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. |
| work_keys_str_mv |
AT chenx rootvectorsofthecompositionalgebraofthekroneckeralgebra |
| first_indexed |
2025-12-07T17:48:25Z |
| last_indexed |
2025-12-07T17:48:25Z |
| _version_ |
1850872645926518784 |