Abstract
Relations between Gorenstein derived categories, Gorenstein defect categories and Gorenstein stable categories are established. Using these, the Gorensteinness of an algebra A and invariants with respect to recollements of the bounded Gorenstein derived category D b gp (A-mod) of A are investigated. Specifically, the Gorensteinness of A is characterized in terms of recollements of D b gp (A-mod) and Gorenstein derived equivalences. It is also shown that Cohen-Macaulay-finiteness is invariant with respect to the recollements of D b gp (A-mod).
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Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant No. 11101259). Some of this work was done when the author was visiting Professor Steffen König in the University of Stuttgart, Germany. The author thanks Steffen König for useful discussions and comments related to this work.
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Gao, N. Gorensteinness, homological invariants and Gorenstein derived categories. Sci. China Math. 60, 431–438 (2017). https://doi.org/10.1007/s11425-015-0781-3
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DOI: https://doi.org/10.1007/s11425-015-0781-3
Keywords
- Gorenstein-projective modules
- CM-finite algebras
- virtually Gorenstein algebras
- Gorenstein derived categories
- Gorenstein defect categories
- Gorenstein stable categories