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Abstract
Let A be a finite-dimensional Gorenstein algebra of finite CM-type. We show that the Gorenstein derived category of A has Auslander–Reiten triangles. In this case, we otain a Serre functor in
. We also establish a relationship between the Nakayama functors and the Gorenstein derived equivalences.
ACKNOWLEDGMENTS
The author sincerely thank the referee for his or her valuable suggestions and comments. The author would like to thank Professor Pu Zhang and Dr. Bao-Lin Xiong for their valuable comments on the work.
Supported by the National Natural Science Foundation of China (Grant No. 10725104), by STCSM (Grant No. 09XD1402500), and by Key Disciplines of Shanghai Municipality (S30104).
Notes
Communicated by Q. Wu.