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ЖУРНАЛЫ // Algebra and Discrete Mathematics // Архив

Algebra Discrete Math., 2004, выпуск 1, страницы 37–56 (Mi adm327)

Эта публикация цитируется в 6 статьях

RESEARCH ARTICLE

Root vectors of the composition algebra of the Kronecker algebra

Xueqing Chen

Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Ave, Ottawa, ON. K1N 6N5, Canada

Аннотация: According to the canonical isomorphism between the positive part $U^+_q(g)$ of the Drinfeld–Jimbo quantum group $U_q (g)$ and the generic composition algebra ${\mathcal C} (\Delta)$ of $\Lambda$, where the Kac–Moody Lie algebra $g$ 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.

Ключевые слова: Quantum group, root vector, Hall algebra, AR-quiver.

MSC: 16G10, 17B37, 16G20, 81R50

Поступила в редакцию: 16.10.2003
Исправленный вариант: 27.01.2004

Язык публикации: английский



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