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

作　　者：DOU RuJing LIU QunHua XIAO Jie 

机构地区：[1]Academy of Mathematics and Systems Science, Chinese Academy of Science, Beijing 100190, China [2]Institute for Algebra and Number Theory, University of Stuttgart, Stuttgart 70569, Germany [3]Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

出　　处：《Science China Mathematics》2011年第2期381-397,共17页中国科学：数学（英文版）

基　　金：supported in part by NSF of China (Grant No. 10631010);NKBRPC (Grant No. 2006CB805905)

摘　　要：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.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.

关 键 词：Ringei-Hall algebra generalized Kac-Moody Lie algebra coherent sheaf semi-stability 

分 类 号：O152.5[理学—数学] O11[理学—基础数学]