On invariability of self-injective algebras of tilted type under stable equivalences

Skowroński, Andrzej; Yamagata, Kunio

doi:10.1090/S0002-9939-03-07134-X

On invariability of self-injective algebras of tilted type under stable equivalences
HTML articles powered by AMS MathViewer

by Andrzej Skowroński and Kunio Yamagata

Proc. Amer. Math. Soc. 132 (2004), 659-667

DOI: https://doi.org/10.1090/S0002-9939-03-07134-X

Published electronically: July 31, 2003

PDF | Request permission

Abstract:

We prove that a large class of self-injective algebras of tilted type is invariant under stable equivalences of module categories.

References

Ibrahim Assem, Jerzy Nehring, and Andrzej Skowroński, Domestic trivial extensions of simply connected algebras, Tsukuba J. Math. 13 (1989), no. 1, 31–72. MR 1003591, DOI 10.21099/tkbjm/1496161006
Maurice Auslander, Idun Reiten, and Sverre O. Smalø, Representation theory of Artin algebras, Cambridge Studies in Advanced Mathematics, vol. 36, Cambridge University Press, Cambridge, 1995. MR 1314422, DOI 10.1017/CBO9780511623608
K. Erdmann, O. Kerner, and A. Skowroński, Self-injective algebras of wild tilted type, J. Pure Appl. Algebra 149 (2000), no. 2, 127–176. MR 1757729, DOI 10.1016/S0022-4049(00)00035-9
P. Gabriel, The universal cover of a representation-finite algebra, Representations of algebras (Puebla, 1980) Lecture Notes in Math., vol. 903, Springer, Berlin-New York, 1981, pp. 68–105. MR 654725
David Hughes and Josef Waschbüsch, Trivial extensions of tilted algebras, Proc. London Math. Soc. (3) 46 (1983), no. 2, 347–364. MR 693045, DOI 10.1112/plms/s3-46.2.347
Andrzej Skowroński, Selfinjective algebras of polynomial growth, Math. Ann. 285 (1989), no. 2, 177–199. MR 1016089, DOI 10.1007/BF01443513
Andrzej Skowroński and Kunio Yamagata, Socle deformations of self-injective algebras, Proc. London Math. Soc. (3) 72 (1996), no. 3, 545–566. MR 1376768, DOI 10.1112/plms/s3-72.3.545
Andrzej Skowroński and Kunio Yamagata, Stable equivalence of selfinjective algebras of tilted type, Arch. Math. (Basel) 70 (1998), no. 5, 341–350. MR 1612578, DOI 10.1007/s000130050205
Andrzej Skowroński and Kunio Yamagata, Galois coverings of selfinjective algebras by repetitive algebras, Trans. Amer. Math. Soc. 351 (1999), no. 2, 715–734. MR 1615962, DOI 10.1090/S0002-9947-99-02362-4
Kunio Yamagata, Representations of nonsplittable extension algebras, J. Algebra 115 (1988), no. 1, 32–45. MR 937600, DOI 10.1016/0021-8693(88)90281-5
Kunio Yamagata, Frobenius algebras, Handbook of algebra, Vol. 1, Handb. Algebr., vol. 1, Elsevier/North-Holland, Amsterdam, 1996, pp. 841–887. MR 1421820, DOI 10.1016/S1570-7954(96)80028-3