413
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Tilting objects in triangulated categories

ORCID Icon, &
Pages 410-429 | Received 23 Sep 2017, Accepted 25 Jun 2019, Published online: 22 Aug 2019

References

  • Angeleri Hügel, L., Coelho, F. U. (2001). Infinitely generated tilting modules of finite projective dimension. Forum Math. 13:239–250. DOI: 10.1515/form.2001.006.
  • Angeleri Hügel, L., Herbera, D., Trlifaj, J. (2006). Tilting modules and Gorenstein rings. Forum Math. 18:211–229. DOI: 10.1515/FORUM.2006.013.
  • Asadollahi, J., Salarian, S. (2004). Gorenstein objects in triangulated categories. J. Algebra 281(1):264–286. DOI: 10.1016/j.jalgebra.2004.07.027.
  • Asadollahi, J., Salarian, S. (2006). Tate cohomology and Gorensteinness for triangulated categories. J. Algebra 299(2):480–502. DOI: 10.1016/j.jalgebra.2005.10.024.
  • Auslander, M. (1974). Representation theory of artin algebras I. Comm. Algebra 1:177–268.
  • Auslander, M., Platzeck, M. I., Reiten, I. (1979). Coxeter functors without diagrams. Trans. Amer. Math. Soc. 250:1–46. DOI: 10.2307/1998978.
  • Beligiannis, A. (2000). Relative homological algebra and purity in triangulated categories. J. Algebra 227(1):268–361. DOI: 10.1006/jabr.1999.8237.
  • Brenner, S., Butler, M. C. R. (1980). Generalizations of the Bernstein–Gelfand–Ponomariev reflection functors. In: Vlastimil Dlab, Peter Gabriel, eds. Proc. ICRA II (Ottawa, 1979). Vol. 832. Berlin: Springer-Verlag, pp. 103–169.
  • Gao, N. (2010). Stable t-structures and homotopy category of Gorenstein-projective modules. J. Algebra 324(9):2503–2511. DOI: 10.1016/j.jalgebra.2010.07.026.
  • Happel, D., Ringel, C. M. (1982). Tilted Algebras. Trans. Amer. Math. Soc. 284:399–443. DOI: 10.2307/1999116.
  • Holm, H. (2004). Gorenstein homological dimensions. Gorenstein homological dimensions. J. Pure Appl. Algebra 189(1–3):167–193. DOI: 10.1016/j.jpaa.2003.11.007.
  • Keller, B. (2007). Derived categories and tilting. In: Angeleri Hügel, L., Happel, D., Krause, H., eds. Handbook of Titing Theory. London Math. Soc. Lecture Note Ser. Vol.332. Cambridge: Cambridge Univ. Press, pp. 49–104.
  • Keller, B. (1994). Deriving DG categories. Ann. Sci. École Norm. Sup. 1(1):63–102. DOI: 10.24033/asens.1689.
  • Martinez-Villa, R., Ortiz-Morales, M. (2014). Tilting theory and functor categories I. Classical tilting. Appl. Categor. Struct. 22:595–646. DOI: 10.1007/s10485-013-9322-y.
  • Martinez-Villa, R., Ortiz-Morales, M. (2013). Tilting theory and functor categories II. Appl. Categor. Struct. 21:311–348. DOI: 10.1007/s10485-011-9266-z.
  • Martinez-Villa, R., Ortiz-Morales, M. (2011). Tilting theory and functor categories III. Int. J. Algebra 5(11):529–561.
  • Mitchell, B. (1972). Rings with several objects. Adv. Math. 8(1):1–161. DOI: 10.1016/0001-8708(72)90002-3.
  • Neeman, A. (2001). Triangulated categories. Ann. Math. Stud. Vol. 148. Princeton: Princeton Univ Press.
  • Ren, W., Liu, Z. K. (2014). Gorenstein homological dimensions for triangulated categories. J. Algebra 410:258–276. DOI: 10.1016/j.jalgebra.2014.03.037.
  • Trlifaj, J. (2001). Cotorsion theories induced by tilting and cotilting modules. Abelian Groups, Rings Modules (Contemp. Math.) 273:285–300.
  • Trlifaj, J. (2007). Infinite dimensional tilting modules and cotorsion pairs. In: Angeleri Hugel, L., Happel, D., Krause, H., eds. Handbook of Tilting Theory, London Math. Soc. Lecture Note Series. Cambridge: Cambridge University Press, 332.
  • Verdier, J. L. (1997). Catégories Dérivées: Etat 0. Lecture Notes in Math. Vol. 569. Berlin: Springer-Verlag, pp. 262–311.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.