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[1]DENNIS R K,IGUSA K. Hochschild homology and the second obstruction for pseudoisotopy[C]//Algebraic K-Theory:Proceedings of a Conference Held at Oberwolfach. Berlin,Heidelberg:Springer,2006:7-58.
[2]LODAY J L. Jean-louis cyclic homology[M]. Berlin:Springer-Verlag,1992.
[3]HAPPEL D. Triangulated categories in the representation of finite dimensional algebras[M]. Cambridge:Cambridge University Press,1988.
[4]HAPPEL D. Reduction techniques for homological conjectures[J]. Tsukuba journal of mathematics,1993,17(1):115-130.
[5]KELLER B. Invariance of cyclic homology under derived equivalence,Representation theory of algebras[M]. Providence,RI:American Mathematical Society,1996.
[6]KELLER B. Derived categories and their uses[J]. Handbook of algebra,1996,1:671-701.
[7]PAN S,XI C. Finiteness of finitistic dimension is invariant under derived equivalences[J]. Journal of algebra,2009,322(1):21-24.
[8]KRAUSE H. Representation type and stable equivalence of Morita type for finite dimensional algebras[J]. Mathematische zeitschrift,1998,229:601-606.
[9]LIU Y,XI C. Constructions of stable equivalences of Morita type for finite dimensional algebras II[J]. Mathematische zeitschrift,2005,251:21-39.
[10]PAN S,ZHOU G. Stable equivalences of Morita type and stable Hochschild cohomology rings[J]. Archiv der mathematik,2010,94(6):511-518.
[11]XI C. Representation dimension and quasi-hereditary algebras[J]. Advances in mathematics,2002,168(2):193-212.
[12]ENOCHS E E,JENDA O M G. Gorenstein injective and projective modules[J]. Mathematische zeitschrift,1995,220(1):611-633.
[13]AUSLANDER M,BRIDGER M. Stable module theory[M]. Providence:American Mathematical Society,1969.
[14]ENOCHS E E,JENDA O M G. Relative homological algebra:Volume 1[M]. Berlin:Walter de Gruyter,GmbH and CO.KG,2011.
[15]GAO N,ZHANG P. Gorenstein derived categories[J]. Journal of algebra,2010,323(7):2041-2057.
[16]HAPPEL D. On gorenstein algebras[C]//Representation Theory of Finite Groups and Finite-Dimensional Algebras:Proceedings of the Conference at the University of Bielefeld from May 15-17,1991,and 7 Survey Articles on Topics of Representation Theory. Birkhäuser Basel,1991:389-404.
[17]RICKARD J. Derived equivalence as derived functors[J]. Journal of London mathematics,1991,43(2):37-48.
[18]HU W,PAN S. Stable functors of derived equivalences and Gorenstein projective modules[J]. Mathematische Nachrichten,2017,290(10):1512-1530.
[19]BEILINSON A A,DELIGNE P. Faisceaux pervers,analysis and topology on singular spaces[M]. Paris:France Mathematical Society,1982.
[20]TADASI NAKAYAMA. On algebras with complete homology[J]. Abhandlungen aus dem mathematischen seminar der universität hamburg,1958(22):300-307.
[21]TACHIKAWA H. On dominant dimensions of algebras[J]. Transactions of the American Mathematical Society,1964,112(2):249-266.
[22]TACHIKAWA H. Quasi-Frobenius Rings and Generalizations[M]. Springer Lecture Notes in Mathematics. Berlin,New York:Springer-Verlag,1973.
[23]MÜLLER B J. The classification of algebras by dominant dimension[J]. Canadian journal of mathematics,1968,20:398-409.
[24]YAMAGATA K. Frobenius algebras[M]. North-Holland,Amsterdam:Elsevier,1996:841-887.
[25]CHEN H,XI C. Dominant dimensions,derived equivalences and tilting modules[J]. Israel journal of mathematics,2016,215:349-395.
[26]CHEN H,FANG M,KERNER O,et al. Rigidity dimension of algebras[C]//Mathematical Proceedings of the Cambridge Philosophical Society. Cambridge:Cambridge University Press,2021,170(2):417-443.
[27]GAO N,KOENIG S. Grade,dominant dimension and Gorenstein algebras[J]. Journal of algebra,2015,427:118-141.
[28]HU W,LUO X H,XIONG B L,et al. Gorenstein projective bimodules via monomorphism categories and filtration categories[J]. Journal of pure and applied algebra,2019,223(3):1014-1039.
[29]BEILINSON A A,GINSBURG V A,SCHECHTMAN V V. Koszul duality[J]. Journal of geometry and physics,1988,5(3):317-350.
[30]HÜGEL L A,KOENIG S,LIU Q,et al. Ladders and simplicity of derived module categories[J]. Journal of algebra,2017,472:15-66.
[31]GAO N,XU X. Homological epimorphisms,compactly generated t-structures and Gorenstein-projective modules[J]. Chinese annals of mathematics(Series B),2018,39:47-58.