과제정보
This work was financially supported by National Natural Science Foundation of China (Grant No.12071120).
참고문헌
- L. Angeleri-Hugel and F. U. Coelho, Infinitely generated tilting modules of finite projective dimension, Forum Math. 13 (2001), no. 2, 239-250. https://doi.org/10.1515/form.2001.006
- J. Asadollahi, P. Bahiraei, R. Hafezi, and R. Vahed, On relative derived categories, Comm. Algebra 44 (2016), no. 12, 5454-5477. https://doi.org/10.1080/00927872.2016.1172618
- M. Auslander and M. Bridger, Stable Module Theory, Memoirs of the American Mathematical Society, No. 94, Amer. Math. Soc., Providence, RI, 1969.
- M. Auslander and R.-O. Buchweitz, The homological theory of maximal Cohen-Macaulay approximations, Mem. Soc. Math. France (N.S.) No. 38 (1989), 5-37.
- M. Auslander and I. Reiten, Applications of contravariantly finite subcategories, Adv. Math. 86 (1991), no. 1, 111-152. https://doi.org/10.1016/0001-8708(91)90037-8
- M. Auslander and O. Solberg, Relative homology and representation theory. I. Relative homology and homologically finite subcategories, Comm. Algebra 21 (1993), no. 9, 2995-3031. https://doi.org/10.1080/00927879308824717
- M. Auslander and O. Solberg, Relative homology and representation theory. II. Relative cotilting theory, Comm. Algebra 21 (1993), no. 9, 3033-3079. https://doi.org/10.1080/00927879308824718
- M. Auslander and O. Solberg, Relative homology and representation theory. III. Cotilting modules and Wedderburn correspondence, Comm. Algebra 21 (1993), no. 9, 3081-3097. https://doi.org/10.1080/00927879308824719
- S. Brenner and M. C. R. Butler, Generalizations of the Bernstein-Gelfand-Ponomarev reflection functors, in Representation theory, II (Proc. Second Internat. Conf., Carleton Univ., Ottawa, Ont., 1979), 103-169, Lecture Notes in Math., 832, Springer, Berlin, 1980.
- A. B. Buan, Subcategories of the derived category and cotilting complexes, Colloq. Math. 88 (2001), no. 1, 1-11. https://doi.org/10.4064/cm88-1-1
- A. B. Buan and Y. Zhou, A silting theorem, J. Pure Appl. Algebra 220 (2016), no. 7, 2748-2770. https://doi.org/10.1016/j.jpaa.2015.12.009
- W. Q. Cao and J. Q. Wei, Gorenstein silting complexes, Glasg. Math. J. 64 (2022), no. 1, 122-135. https://doi.org/10.1017/S0017089520000646
- L. W. Christensen, A. Frankild, and H. Holm, On Gorenstein projective, injective and flat dimensions-a functorial description with applications, J. Algebra 302 (2006), no. 1, 231-279. https://doi.org/10.1016/j.jalgebra.2005.12.007
- R. R. Colby and K. R. Fuller, Equivalence and duality for module categories, Cambridge Tracts in Mathematics, 161, Cambridge Univ. Press, Cambridge, 2004. https://doi.org/10.1017/CBO9780511546518
- R. Colpi and J. Trlifaj, Tilting modules and tilting torsion theories, J. Algebra 178 (1995), no. 2, 614-634. https://doi.org/10.1006/jabr.1995.1368
- E. E. Enochs and O. M. G. Jenda, Gorenstein injective and projective modules, Math. Z. 220 (1995), no. 4, 611-633. https://doi.org/10.1007/BF02572634
- E. E. Enochs and O. M. G. Jenda, Relative Homological Algebra, De Gruyter Expositions in Mathematics, 30. Walter de Gruyter & Co., Berlin. 2000.
- N. Gao and P. Zhang, Gorenstein derived categories, J. Algebra 323 (2010), no. 7, 2041-2057. https://doi.org/10.1016/j.jalgebra.2010.01.027
- D. Happel and C. M. Ringel, Tilted algebras, Trans. Amer. Math. Soc. 274 (1982), no. 2, 399-443. https://doi.org/10.2307/1999116
- M. Hoshino, Y. Kato, and J. Miyachi, On t-structures and torsion theories induced by compact objects, J. Pure Appl. Algebra 167 (2002), no. 1, 15-35. https://doi.org/10.1016/S0022-4049(01)00012-3
- B. Keller, Derived categories and their uses, in Handbook of algebra, Vol. 1, 671-701, Handb. Algebr., 1, Elsevier/North-Holland, Amsterdam, 1996. https://doi.org/10.1016/S1570-7954(96)80023-4
- B. Keller and D. Vossieck, Aisles in derived categories, Bull. Soc. Math. Belg. Ser. A 40 (1988), no. 2, 239-253.
- H. Koga, On partial tilting complexes, Comm. Algebra 39 (2011), no. 7, 2417-2429. https://doi.org/10.1080/00927872.2010.488685
- J. Miyachi, Extensions of rings and tilting complexes, J. Pure Appl. Algebra 105 (1995), no. 2, 183-194. https://doi.org/10.1016/0022-4049(94)00145-6
- P. Moradifar and S. Yassemi, Infinitely generated Gorenstein tilting modules, Algebr. Represent. Theory 25 (2022), no. 6, 1389-1427. https://doi.org/10.1007/s10468-021-10072-8
- J. Rickard, Morita theory for derived categories, J. London Math. Soc. (2) 39 (1989), no. 3, 436-456. https://doi.org/10.1112/jlms/s2-39.3.436
- J. Rickard, Derived categories and stable equivalence, J. Pure Appl. Algebra 61 (1989), no. 3, 303-317. https://doi.org/10.1016/0022-4049(89)90081-9
- J.-L. Verdier, Des categories derivees des categories abeliennes, Asterisque No. 239 (1996), xii+253 pp.
- J. Q. Wei, A note on relative tilting modules, J. Pure Appl. Algebra 214 (2010), no. 4, 493-500. https://doi.org/10.1016/j.jpaa.2009.06.018
- J. Q. Wei, Semi-tilting complexes, Israel J. Math. 194 (2013), no. 2, 871-893. https://doi.org/10.1007/s11856-012-0093-1
- L. Yan, W. Li, and B. Ouyang, Gorenstein cotilting and tilting modules, Comm. Algebra 44 (2016), no. 2, 591-603. https://doi.org/10.1080/00927872.2014.981752
- P. Zhang and J. Q. Wei, Cosilting complexes and AIR-cotilting modules, J. Algebra 491 (2017), 1-31. https://doi.org/10.1016/j.jalgebra.2017.07.022