Abstract
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 \(F: D^b(A) \longrightarrow T(A)^{\mathbb{Z}}\mbox{-}\underline{\rm mod}\).
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Dedicated to Professor Zhe-Xian Wan on the occasion of his eightieth birthday
Supported by the National Natural Science Foundation of China (Grant No. 10301033) and of Shanghai City (Grant No. ZR0614049).