Abstract
In this paper, we study the category ℋ (ρ) of semi-stable coherent sheaves of a fixed slope ρ 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 ℋ (ρ) 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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Dou, R., Liu, Q. & Xiao, J. The double Ringel-Hall algebra on a hereditary abelian finitary length category. Sci. China Math. 54, 381–397 (2011). https://doi.org/10.1007/s11425-010-4143-z
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DOI: https://doi.org/10.1007/s11425-010-4143-z