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arXiv · 0908.1666

The double Ringel-Hall algebra on a hereditary abelian finitary length category

Rujing Dou·Qunhua Liu·Jie Xiao
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Abstract

In this paper, we study the category $\mathscr{H}^{(\rho)}$ of semi-stable coherent sheaves of a fixed slope $\rho$ over a weighted projective curve. This category has nice properties: it is a hereditary abelian finitary length category. We will define the Ringel-Hall algebra of $\mathscr{H}^{(\rho)}$ and relate it to generalized Kac-Moody Lie algebras. Finally we obtain the Kac type theorem to describe the indecomposable objects in this category, i.e. the indecomposable semi-stable sheaves.

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BibTeXRIS

Rujing Dou, Qunhua Liu, Jie Xiao. 2009-08-12. The double Ringel-Hall algebra on a hereditary abelian finitary length category. https://doi.org/10.1007/s11425-010-4143-z

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