On tilting and cotilting-type modules

Gabriella D'Este

Commentationes Mathematicae Universitatis Carolinae (2005)

  • Volume: 46, Issue: 2, page 281-291
  • ISSN: 0010-2628

Abstract

top
We use modules of finite length to compare various generalizations of the classical tilting and cotilting modules introduced by Brenner and Butler [BrBu].

How to cite

top

D'Este, Gabriella. "On tilting and cotilting-type modules." Commentationes Mathematicae Universitatis Carolinae 46.2 (2005): 281-291. <http://eudml.org/doc/249524>.

@article{DEste2005,
abstract = {We use modules of finite length to compare various generalizations of the classical tilting and cotilting modules introduced by Brenner and Butler [BrBu].},
author = {D'Este, Gabriella},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {tilting and cotilting modules; quivers and Auslander-Reiten quivers; tilting modules; cotilting modules; Auslander-Reiten quivers},
language = {eng},
number = {2},
pages = {281-291},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On tilting and cotilting-type modules},
url = {http://eudml.org/doc/249524},
volume = {46},
year = {2005},
}

TY - JOUR
AU - D'Este, Gabriella
TI - On tilting and cotilting-type modules
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 2
SP - 281
EP - 291
AB - We use modules of finite length to compare various generalizations of the classical tilting and cotilting modules introduced by Brenner and Butler [BrBu].
LA - eng
KW - tilting and cotilting modules; quivers and Auslander-Reiten quivers; tilting modules; cotilting modules; Auslander-Reiten quivers
UR - http://eudml.org/doc/249524
ER -

References

top
  1. Anderson F.W., Fuller K.R., Rings and Categories of Modules, GTM 13, Springer, New York, 1992. Zbl0765.16001MR1245487
  2. Angeleri Hügel L., Trlifaj J., Direct limits of modules of finite projective dimension, Proc. Algebra Conf. Venezia 2002, Lecture Notes in Pure and Appl. Math. 236, Dekker, New York, 2004, pp.27-44. MR2050699
  3. Angeleri Hügel L., Tonolo A., Trlifaj J., Tilting preenvelopes and cotilting precovers, Algebr. Represent. Theory 4 (2001), 155-170. (2001) Zbl0999.16007MR1834843
  4. Auslander M., Reiten I., Smalø S.O., Representation theory of Artin algebras, Cambridge University Press, Cambridge, 1995, . MR1314422
  5. Bazzoni S., Cotilting modules are pure-injective, Proc. Amer. Math. Soc. 131 12 (2003), 3665-3672. (2003) Zbl1045.16004MR1998172
  6. Bazzoni S., A characterization of n -cotilting and n -tilting modules, J. Algebra 273 (2004), 359-372. (2004) Zbl1051.16007MR2032465
  7. Bazzoni S., n -cotilting modules and pure-injectivity, Bull. London Math. Soc. 36 5 (2004), 599-612. (2004) Zbl1085.16004MR2070436
  8. Buan A.B., Krause H., Cotilting modules over tame hereditary algebras, Pacific J. Math. 211 1 (2003), 41-59. (2003) Zbl1070.16014MR2016589
  9. Brenner S., Butler M.C.R., Generalizations of the Bernstein-Gelfand-Ponomarev Reflection Functors, Lecture Notes in Mathematics 832, Springer, Berlin-New York, 1980, pp.103-169. Zbl0446.16031MR0607151
  10. Buan A.B., Solberg Ø., Relative cotilting theory and almost complete cotilting modules, CMS Conf. Proc. 24, Amer. Math. Soc., Providence, 1998, pp.77-92. Zbl0926.16013MR1648616
  11. Colpi R., Tilting modules and * -modules, Comm. Algebra 21.4 (1993), 1095-1102. (1993) MR1209922
  12. Colpi R., Dualities induced by cotilting bimodules, Proc. Algebra Conf. Venezia 2002, Lecture Notes in Pure and Appl. Math. 236, Dekker, New York, 2004, pp.89-102. Zbl1072.16008MR2050704
  13. Colby R.R., Fuller K.R., Weak Morita duality, Comm. Algebra 31 (2003), 1859-1879. (2003) Zbl1027.16008MR1972896
  14. Colpi R., D'Este G., Tonolo A., Quasi-tilting modules and counter equivalences, J. Algebra 191 (1997), 461-494. (1997) Zbl0876.16004MR1448804
  15. Colpi R., D'Este G., Tonolo A., Corrigendum, J. Algebra 206 (1998), 370. (1998) MR1637300
  16. Coelho F.U., Happel D., Unger L., Complements to partial tilting modules, J. Algebra 170 (1994), 184-205. (1994) Zbl0834.16012MR1302837
  17. D'Este G., Symmetries and Asymmetries for Cotilting Bimodules, Proc. Algebra Conf. Venezia 2002, Lecture Notes in Pure and Appl. Math. 236, Dekker, New York, 2004, pp.103-118. Zbl1072.16009MR2050705
  18. Gregorio E., Tilting theory for comodules, preprint, 2002. 
  19. Happel D., Ringel C.M., Construction of Tilted Algebras, Lecture Notes in Mathematics 903, Springer, Berlin-New York, 1981, pp.125-144. Zbl0503.16025MR0654707
  20. Happel D., Unger L., Complements and the Generalized Nakayama Conjecture, CMS Conf. Proc. 24, Amer. Math. Soc., Providence, 1998, pp.293-310. Zbl0944.16010MR1648633
  21. Huisgen-Zimmermann B., Purity, algebraic compactness, direct sum decompositions, and representation type, Infinite Length Modules (H. Krause and C.M. Ringel, Eds.), Proceedings of the Euroconference, Bielefeld 1998, Birkhäuser, 2000, pp.331-367. Zbl0990.16004MR1789225
  22. Jensen C.U., Lenzing H., Model Theoretic Algebra, Gordon and Breach Science Publishers, New York, 1989. Zbl0728.03026MR1057608
  23. Krause H., Saorìn M., On minimal approximations of modules, Contemp. Math. 229 (1998), 227-236. (1998) MR1676223
  24. Ringel C.M., Tame Algebras and Integral Quadratic Forms, Lecture Notes in Mathematics 1099, Springer, Berlin, 1984. Zbl0546.16013MR0774589
  25. Ringel C.M., Infinite length modules: some examples as introduction, Infinite Length Modules (H. Krause and C.M. Ringel, Eds.), Proceedings of the Euroconference, Bielefeld 1998, Birkhäuser, 2000, pp.1-73. Zbl0988.16002MR1789209
  26. Reiten I., Ringel C.M., Infinite dimensional representations of canonical algebras, preprint, 2002. MR2195596

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.