Left-sided quasi-invertible bimodules over Nakayama algebras

Zygmunt Pogorzały

Open Mathematics (2005)

  • Volume: 3, Issue: 1, page 125-142
  • ISSN: 2391-5455

Abstract

top
Bimodules over triangular Nakayama algebras that give stable equivalences of Morita type are studied here. As a consequence one obtains that every stable equivalence of Morita type between triangular Nakayama algebras is a Morita equivalence.

How to cite

top

Zygmunt Pogorzały. "Left-sided quasi-invertible bimodules over Nakayama algebras." Open Mathematics 3.1 (2005): 125-142. <http://eudml.org/doc/268743>.

@article{ZygmuntPogorzały2005,
abstract = {Bimodules over triangular Nakayama algebras that give stable equivalences of Morita type are studied here. As a consequence one obtains that every stable equivalence of Morita type between triangular Nakayama algebras is a Morita equivalence.},
author = {Zygmunt Pogorzały},
journal = {Open Mathematics},
keywords = {16D20; 16G20},
language = {eng},
number = {1},
pages = {125-142},
title = {Left-sided quasi-invertible bimodules over Nakayama algebras},
url = {http://eudml.org/doc/268743},
volume = {3},
year = {2005},
}

TY - JOUR
AU - Zygmunt Pogorzały
TI - Left-sided quasi-invertible bimodules over Nakayama algebras
JO - Open Mathematics
PY - 2005
VL - 3
IS - 1
SP - 125
EP - 142
AB - Bimodules over triangular Nakayama algebras that give stable equivalences of Morita type are studied here. As a consequence one obtains that every stable equivalence of Morita type between triangular Nakayama algebras is a Morita equivalence.
LA - eng
KW - 16D20; 16G20
UR - http://eudml.org/doc/268743
ER -

References

top
  1. [1] M. Auslander and I. Reiten: “On a Theorem of E. Green on the Dual of the Transpose”, Proc. ICRA V, CMS Conf. Proc., Vol. 11, (1991), pp. 53–65. 
  2. [2] M. Broué: “Equivalences of Blocks of Group Algebras”, In: V. Dlab and L.L. Scott (Eds.): Finite Dimensional Algebras and Related Topics, NATO ASI Series C, Vol. 424, Kluwer Academic Press, Dodrecht, 1992, pp. 1–26. 
  3. [3] P. Gabriel: Auslander-Reiten sequences and representation-finite algebras, Springer Lecture Notes in Math., Vol. 831, Berlin, 1980, pp. 1–71. http://dx.doi.org/10.1007/BFb0089778 Zbl0445.16023
  4. [4] D. Happel: “Hochschild cohomology of finite-dimensional algebras”, In: Seminaire d’Algebre P. Dubriel et M-P. Maliavin, Lecture Notes in Math., Vol. 1404, Springer, Berlin, 1989, pp. 108–126. 
  5. [5] S. MacLane: Homology, Springer-Verlag, Berlin, 1963. 
  6. [6] K. Morita: “Duality for modules and its applications to the theory of rings with minimum condition”, Sci. Rep. Tokyo Kyoiku Daigaku Sec. A, Vol. 6, (1958), pp. 83–142. 
  7. [7] Z. Pogorzały: “Algebras stably equivalent to selfinjective special biserial algebras”, Comm. Algebra, Vol. 22, (1994), pp. 1127–1160. Zbl0805.16008
  8. [8] Z. Pogorzały: “Left-right projective bimodules and stable equivalence of Morita type”, Colloq. Math., Vol. 88(2), (2001), pp. 243–255. Zbl0985.16004
  9. [9] Z. Pogorzały and A. Skowroński: “On algebras whose indecomposable modules are multiplicity-free”, Proc. London Math. Soc., Vol. 47, (1983), pp. 463–479. Zbl0559.16016
  10. [10] J. Rickard: “Derived equivalences as derived functors”, J. London. Math. Soc., Vol. 2(43), (1991), pp. 37–48. Zbl0683.16030
  11. [11] J. Rickard: “Some Recent Advances in Modular Representation Theory”, Proc. ICRA VIII, CMS Conf. Proc., Vol. 23, (1998), pp. 157–178. Zbl0914.20010
  12. [12] C.M. Ringel: Tame Algebras and Integral Quadratic Forms, Springer Lecture Notes in Math., Vol. 1099, Berlin, 1984. 
  13. [13] D. Simson: Linear Representations of Partially Ordered Sets and Vector Space Categories, Gordon & Breach Science Publishers, Amsterdam, 1992. Zbl0818.16009

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.