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2003 | 1 | 4 | 457-476
Tytuł artykułu

Domestic iterated one-point extensions of algebras by two-ray modules

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the paper, we introduce a wide class of domestic finite dimensional algebras over an algebraically closed field which are obtained from the hereditary algebras of Euclidean type , n≥1, by iterated one-point extensions by two-ray modules. We prove that these algebras are domestic and their Auslander-Reiten quivers admit infinitely many nonperiodic connected components with infinitely many orbits with respect to the action of the Auslander-Reiten translation. Moreover, we exhibit a wide class of almost sincere domestic simply connected algebras of large global dimensions.
Wydawca
Czasopismo
Rocznik
Tom
1
Numer
4
Strony
457-476
Opis fizyczny
Daty
wydano
2003-12-01
online
2003-12-01
Twórcy
Bibliografia
  • [1] I. Assem and A. Skowroński: “On some classes of simply connected algebras”, Proc. London Math. Soc., Vol. 56, (1988), pp. 417–450.
  • [2] M. Auslander, I. Reiten, S. Smalø: Representation theory of Artin algebras, Cambridge Studies in Advanced Mathematics 36, Cambridge University Press, Cambridge, 1995.
  • [3] G. Bobiński, P. Dräxler, A. Skowroński: “Domestic algebras with many nonperiodic Auslander-Reiten components”, Comm. Algebra, Vol. 31, (2003), pp. 1881–1926. http://dx.doi.org/10.1081/AGB-120018513
  • [4] G. Bobiński and A. Skowroński: “On a family of vector space categories”, Cent. Eur. J. Math., Vol. 3, (2003), pp. 332–359. preprint, Toruń, 2002. http://dx.doi.org/10.2478/BF02475214
  • [5] M.C.R. Butler and C.M. Ringel: “Auslander-Reiten sequences with few middle terms and applications to string algebras”, Comm. Algebra, Vol. 15, (1987), pp. 145–179.
  • [6] W. Crawley-Boevey: “Tame algebras and generic modules”, Proc. London Math. Soc., Vol. 63, (1991), pp. 241–265.
  • [7] Yu.A. Drozd: “Tame and wild matrix problems”, In: Representation Theory II, Lecture Notes in Math. 832 Springer-Verlag, Berlin-New York, 1980, pp. 242–258.
  • [8] P. Malicki, A. Skowroński, B. Tomé: “Indecomposable modules in coils”, Colloq. Math., Vol. 93, (2002), pp. 67–130. http://dx.doi.org/10.4064/cm93-1-7
  • [9] J.A. de la Peña: “Tame algebras with sincere directing modules”, J. Algebra, Vol. 161, (1993), pp. 171–185. http://dx.doi.org/10.1006/jabr.1993.1211
  • [10] J.A. de la Peña and A. Skowroński: “Geometric and homological characterizations of polynomial growth strongly simply connected algebras”, Invent. Math., Vol. 126, (1996), pp. 287–296. http://dx.doi.org/10.1007/s002220050100
  • [11] C.M. Ringel: “Tame algebras”, In: Representation Theory I, Lecture Notes in Math. 831, Springer-Verlag, Berlin-New York, 1980, pp. 134–287.
  • [12] C.M. Ringel: Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer-Verlag, Berlin-New York, 1984.
  • [13] D. Simson: Linear Representations of Partially Ordered Sets and Vector Space Categories, Algebra, Logic and Appl. 4, Gordon and Breach, Montreux, 1992.
  • [14] A. Skowroński: Algebras of polynomial growth, in: Topics in Algebra, Part 1, Banach Center Publications 26, PWN, Warsaw, 1990, pp. 535–568.
  • [15] A. Skowroński: “Simply connected algebras of polynomial growth”, Compositio Math., Vol. 109, (1997), pp. 99–133. http://dx.doi.org/10.1023/A:1000245728528
  • [16] A. Skowroński: “Tame algebras with strongly simply connected Galois coverings”, Colloq. Math., Vol. 72, (1997), pp. 335–351.
  • [17] A. Skowroński and G. Zwara: “On the numbers of discrete indecomposable modules over tame algebras”, Colloq. Math., Vol. 73, (1997), pp. 93–114.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_BF02475179
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