Root Categories and Simple Lie Algebras

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• 作者：Peng ; Liangang ; Xiao ; Jie
• 刊名：Journal of Algebra
• 出版年：1997
• 出版时间：December 1, 1997
• 年：1997
• 卷：198
• 期：1
• 页码：19-56
• 全文大小：412 K

文摘

By using theT²-orbit category of the derived category of a hereditary algebra, which is proved to be a triangulated category too, we give a complete realization of a simple Lie algebra. This is a global version of Ringel's work for the positive parts of simple Lie algebras. In this realization, the Grothendieck group provides the Cartan subalgebra, the indecomposable objects correspond to the Chevalley basis, and the structure constants are given by the evaluations of Hall polynomials.