151
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Stable Projective Homotopy Theory of Modules, Tails, and Koszul Duality

&
Pages 3941-3973 | Received 13 Mar 2009, Published online: 24 Nov 2010

REFERENCES

  • Bernstein , I. N. , Gelfand , I. M. , Gelfand , S. I. ( 1978 ). Algebraic vector bundles on P n and problems of linear algebra . Funktsional. Anal. i Prilozhen. 12 ( 3 ): 66 – 67 .
  • Bourbaki , N. ( 1980 ). Éléments de Mathématique. Algèbre. Chapitre X . Paris : Masson .
  • Gelfand , S. I. , Manin , Y. I. ( 2003 ). Methods of Homological Algebra. , 2nd ed. Springer Monographs in Mathematics. Berlin : Springer-Verlag .
  • Green , E. L. ( 1997 ). Introduction to Koszul algebras . In: Representation Theory and Algebraic Geometry (Waltham, MA, 1995). Volume 238 of London Math. Soc. Lecture Note Ser . Cambridge : Cambridge Univ. Press , pp. 45 – 62 .
  • Green , E. L. , Martínez Villa , R. (1996). Koszul and Yoneda algebras. In: Representation Theory of Algebras (Cocoyoc, 1994). Volume 18 of CMS Conf. Proc . Providence , RI : Amer. Math. Soc., pp. 247–297.
  • Green , E. L. , Martínez-Villa , R. ( 1998 ). Koszul and Yoneda algebras. II . In: Algebras and Modules, II (Geiranger, 1996). Volume 24 of CMS Conf. Proc. , Providence , RI : Amer. Math. Soc. , pp. 227 – 244 .
  • Martínez-Villa , R. ( 1998 ). Serre duality for generalizAuslander regular algebras . In: Trends in the Representation Theory of Finite-Dimensional Algebras (Seattle, WA, 1997). Volume 229 of Contemp. Math . Providence , RI : Amer. Math. Soc. , pp. 237 – 263 .
  • Martínez Villa , R. , Martsinkovsky , A. ( 2004 ). Cohomology of tails, Tate-Vogel cohomology, and noncommutative Serre duality over Koszul quiver algebras . J. Algebra 280 ( 1 ): 58 – 83 .
  • Martínez Villa , R. , Martsinkovsky , A. ( 2005 ). The Gabriel-Serre category, the Tate–Vogel category, and Koszul duality . In: Representation Theory of Finite-Dimensional Algebras . Oberwolfach Rep. 2, No. 1, Report 6 , pp. 375 – 376 .
  • Martínez Villa , R. , Saorín , M. ( 2004 ). Koszul equivalences and dualities . Pacific J. Math. 214 ( 2 ): 359 – 378 .
  • Martínez-Villa , R. , Zacharia , D. ( 2003 ). Approximations with modules having linear resolutions . J. Algebra 266 ( 2 ): 671 – 697 .
  • Mazorchuk , S. , Ovsienko , V. , Stroppel , C. ( 2006 ). Quadratic Duals, Koszul Dual Functors, and Applications . Preprint, Uppsala University, Uppsala. 50 pp .
  • Neeman , A. ( 2001 ). Triangulated Categories. Volume 148 of Annals of Mathematics Studies. Princeton , NJ : Princeton University Press .
  • Verdier , J.-L. ( 1996 ). Des catégories dérivées des catégories abéliennes. Astérisque, (239):xii+ 253 pp. (1997), With a preface by Luc Illusie, Edited and with a note by Georges Maltsiniotis .
  • Communicated by D. Zacharia.
  • To Kent Fuller, a friend and a teacher.

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.