A note on tilting sequences

Clezio Braga; Flávio Coelho

Open Mathematics (2008)

  • Volume: 6, Issue: 3, page 364-371
  • ISSN: 2391-5455

Abstract

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We discuss the existence of tilting modules which are direct limits of finitely generated tilting modules over tilted algebras.

How to cite

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Clezio Braga, and Flávio Coelho. "A note on tilting sequences." Open Mathematics 6.3 (2008): 364-371. <http://eudml.org/doc/269057>.

@article{ClezioBraga2008,
abstract = {We discuss the existence of tilting modules which are direct limits of finitely generated tilting modules over tilted algebras.},
author = {Clezio Braga, Flávio Coelho},
journal = {Open Mathematics},
keywords = {tilting modules; direct limits; tilted algebras; connected hereditary algebras; connected components; Auslander-Reiten quivers; indecomposable summands},
language = {eng},
number = {3},
pages = {364-371},
title = {A note on tilting sequences},
url = {http://eudml.org/doc/269057},
volume = {6},
year = {2008},
}

TY - JOUR
AU - Clezio Braga
AU - Flávio Coelho
TI - A note on tilting sequences
JO - Open Mathematics
PY - 2008
VL - 6
IS - 3
SP - 364
EP - 371
AB - We discuss the existence of tilting modules which are direct limits of finitely generated tilting modules over tilted algebras.
LA - eng
KW - tilting modules; direct limits; tilted algebras; connected hereditary algebras; connected components; Auslander-Reiten quivers; indecomposable summands
UR - http://eudml.org/doc/269057
ER -

References

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  2. [2] Assem I., Simson D., Skowroński A., Elements of the representation theory of associative algebras, London Mathematical Society Student Texts 65, Cambridge University Press, Cambridge, 2006 Zbl1092.16001
  3. [3] Auslander M., Platzeck M.I., Reiten I., Coxeter functors without diagrams, Trans. Amer. Math. Soc., 1979, 250, 1–46 http://dx.doi.org/10.2307/1998978 Zbl0421.16016
  4. [4] Auslander M., Reiten I., Smalø S., Representation theory of Artin algebras, Cambridge Studies in Advanced Mathematics 36, Cambridge University Press, Cambridge, 1995 Zbl0834.16001
  5. [5] Bazzoni S., Stovícek J., All tilting modules are of finite type, Proc. Amer. Math. Soc., to appear Zbl1132.16008
  6. [6] Braga C., Coelho F.U., Limits of tilting modules, preprint Zbl1228.16009
  7. [7] Brenner S., Butler M.C.R., Generalizations of the Bernstein-Gelfand-Ponomarev reflection functors, Proc. Second Internat. Conf. Carleton Univ. (1979 Ottawa Canada), Lecture Notes in Math. 832, Springer, Berlin-New York, 1980, 103–169 Zbl0446.16031
  8. [8] Buan A., Solberg O., Limits of pure-injective cotilting modules, Algebr. Represent. Theory, 2005, 8, 621–634 http://dx.doi.org/10.1007/s10468-005-0341-8 Zbl1099.16003
  9. [9] Eklof P., Trlifaj J., How to make Ext vanish, Bull. London Math. Soc., 2001, 33, 41–51 http://dx.doi.org/10.1112/blms/33.1.41 Zbl1030.16004
  10. [10] Happel D., Ringel C.M., Tilted algebras, Trans. Amer. Math. Soc., 1982, 274, 399–443 http://dx.doi.org/10.2307/1999116 Zbl0503.16024
  11. [11] Liu S., Tilted algebras and generalized standard Auslander-Reiten components, Arch. Math., 1993, 61, 12–19 http://dx.doi.org/10.1007/BF01258050 Zbl0809.16015
  12. [12] Skowroński A., Generalized standard Auslander-Reiten components without oriented cycles, Osaka J. Math., 1993, 30, 515–527 Zbl0818.16017
  13. [13] Skowroński A., Minimal representation-infinite Artin algebras, Math. Proc. Cambridge Philos. Soc., 1994, 116, 229–243 http://dx.doi.org/10.1017/S0305004100072546 Zbl0822.16010

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