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2004 | 2 | 1 | 103-111
Tytuł artykułu

Finiteness of the strong global dimension of radical square zero algebras

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Języki publikacji
EN
Abstrakty
EN
The strong global dimension of a finite dimensional algebra A is the maximum of the width of indecomposable bounded differential complexes of finite dimensional projective A-modules. We prove that the strong global dimension of a finite dimensional radical square zero algebra A over an algebraically closed field is finite if and only if A is piecewise hereditary. Moreover, we discuss results concerning the finiteness of the strong global dimension of algebras and the related problem on the density of the push-down functors associated to the canonical Galois coverings of the trivial extensions of algebras by their repetitive algebras.
Wydawca
Czasopismo
Rocznik
Tom
2
Numer
1
Strony
103-111
Opis fizyczny
Daty
wydano
2004-03-01
online
2004-03-01
Twórcy
autor
autor
Bibliografia
  • [1] I. Assem, J. Nehring and A. Skowroński, “Domestic trivial extensions of simply connected algebras”, Tsukuba J. Math., Vol. 13, (1989), pp. 31–72.
  • [2] I. Assem and A. Skowroński, “Algebras with cycle-finite derived categories”, Math. Ann., Vol. 280, (1988), pp. 441–463. http://dx.doi.org/10.1007/BF01456336
  • [3] I. Assem and A. Skowroński, “On tame repetitive algebras”, Fund. Math., Vol. 142, (1993), pp. 59–84.
  • [4] K. Bongartz and P. Gabriel, “Covering spaces in representations theory”, Invent. Math., Vol. 65, (1982), pp. 331–378. http://dx.doi.org/10.1007/BF01396624
  • [5] P. Dowbor and A. Skowroński, “On Galois coverings of tame algebras”, Arch. Math., Vol. 44, (1985), pp. 522–529. http://dx.doi.org/10.1007/BF01193992
  • [6] P. Dowbor and A. Skowroński, “Galois coverings of representation-infinite algebras”, Comment. Math. Helv., Vol. 62, (1987), pp. 311–337.
  • [7] K. Erdmann, O. Kerner and A. Skowroński, “Self-injective algebras of wild tilted type”, J. Pure Appl. Algebra, Vol. 149, (2000), pp. 127–176. http://dx.doi.org/10.1016/S0022-4049(00)00035-9
  • [8] P. Gabriel, “The universal cover of a representation-finite algebra” In: Representations of Algebras, Lecture Notes in Math., Vol. 903, Springer, 1981, pp. 68–105.
  • [9] E.L. Green, “Graphs with relations, coverings and group graded algebras”, Trans. Amer. Math. Soc., Vol. 279, (1983), pp. 297–310. http://dx.doi.org/10.2307/1999386
  • [10] D. Happel, “On the derived category of a finite dimensional algebra”, Comment. Math. Helv, Vol. 62, (1987), pp. 339–389.
  • [11] D. Happel, “A characterization of hereditary categories with tilting object”, Invent. Math., Vol. 144, (2001), pp. 381–398. http://dx.doi.org/10.1007/s002220100135
  • [12] D. Happel, I. Reiten and S.O. Smalø, Tilting in abelian categories and quasitilted algebras, Mem. Amer. Math. Soc., Providence, Rhode Island, 1996.
  • [13] D. Happel, I. Reiten and S.O. Smalø, “Piecewise hereditary algebras”, Arch. Math., Vol. 66, (1996), pp. 182–186. http://dx.doi.org/10.1007/BF01195702
  • [14] D. Happel, J. Rickard and A. Schofield, “Piecewise hereditary algebras”, Bull. London Math. Soc., Vol. 20, (1988), pp. 23–28.
  • [15] D. Hughes and J. Waschbüsch, “Trivial extensions of tilted algebras”, Proc. London Math. Soc., Vol. 46, (1983), pp. 347–364.
  • [16] H. Lenzing and A. Skowroński, “Selfinjective algebras of wild canonical type”, Colloq. Math., Vol. 96, (2003), pp. 245–275. http://dx.doi.org/10.4064/cm96-2-9
  • [17] J. Nehring and A. Skowroński, “Polynomial growth trivial extensions of simply connected algebras”, Fund. Math., Vol. 132, (1989), pp. 117–134.
  • [18] C.M. Ringel, Tame algebras and integral guadratic forms, Lecture Notes in Math., Springer, Berlin, 1984.
  • [19] J. Schröer, “On the quiver with relations of a repetitive algebra”, Arch. Math., Vol. 72, (1999), pp. 426–432. http://dx.doi.org/10.1007/s000130050351
  • [20] A. Skowroński, “Generalization of Yamagata’s theorem on trivial extensions”, Arch. Math., Vol. 48, (1987), pp. 68–76. http://dx.doi.org/10.1007/BF01196357
  • [21] A. Skowroński, “On algebras with finite strong global dimension”, Bull. Polish. Acad. Sci., Vol. 35, (1987), pp. 539–547.
  • [22] A. Skowroński, “Tame quasi-tilted algebras”, J. Algebra, Vol. 203, (1998), pp. 470–490. http://dx.doi.org/10.1006/jabr.1997.7328
  • [23] K. Yamagata, “On algebras whose trivial extensions are of finite representation type”, In: Representations of Algebras, Lecture Notes in Math., Vol. 903, Springer, 1981, pp. 364–371.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_BF02475954
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