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Abstract
The paper is devoted to study some of the questions arises naturally in connection to the notion of relative derived categories. In particular, we study invariants of recollements involving relative derived categories, generalize two results of Happel by proving the existence of AR-triangles in Gorenstein-derived categories, provide situations for which relative derived categories with respect to Gorenstein projective and Gorenstein injective modules are equivalent, and finally study relations between the Gorenstein-derived category of a quiver and its image under a reflection functor. Some interesting applications are provided.
ACKNOWLEDGMENTS
The authors would like to thank the referees for their useful hints and comments that improved our exposition. The first author also thanks the IMU-Simons Foundation Travel Fellowship for providing a travel grant to visit MPIM. He also thanks the Center of Excellence for Mathematics (University of Isfahan). This research was in part supported by a grant from IPM (No: 93130216).