Quotient triangulated categories

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• 作者：Xiao-Wu Chen and Pu Zhang
• 关键词：Mathematics Subject Classification (2000) 16G10 ; 16E65
• 刊名：manuscripta mathematica
• 出版年：2007
• 出版时间：June, 2007
• 年：2007
• 卷：123
• 期：2
• 页码：167-183
• 全文大小：229 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Algebraic Geometry
  Topological Groups and Lie Groups
  Geometry
  Number Theory
  Calculus of Variations and Optimal Control
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1785

文摘

For a self-orthogonal module T, the relation between the quotient triangulated category D b (A)/K b (addT) and the stable category of the Frobenius category of T-Cohen-Macaulay modules is investigated. In particular, for a Gorenstein algebra, we get a relative version of the description of the singularity category due to Happel. Also, the derived category of a Gorenstein algebra is explicitly given, inside the stable category of the graded module category of the corresponding trivial extension algebra, via Happel’s functor F: Db(A) ? T(A)\mathbbZ-modF: D^b(A) \longrightarrow T(A)^{\mathbb{Z}}\mbox{-}\underline{\rm mod}.