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1994 | 144 | 2 | 143-161
Tytuł artykułu

On the representation type of tensor product algebras

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The representation type of tensor product algebras of finite-dimensional algebras is considered. The characterization of algebras A, B such that A ⊗ B is of tame representation type is given in terms of the Gabriel quivers of the algebras A, B.
Słowa kluczowe
Rocznik
Tom
144
Numer
2
Strony
143-161
Opis fizyczny
Daty
wydano
1994
otrzymano
1992-10-28
poprawiono
1993-04-30
poprawiono
1993-09-28
Twórcy
  • Institute of Mathematics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
Bibliografia
  • [AS] I. Assem and A. Skowroński, On some classes of simply connected algebras, Proc. London Math. Soc. 56 (1988), 417-450.
  • [AR] M. Auslander and I. Reiten, On the representation type of triangular matrix rings, J. London Math. Soc. (2) 12 (1976), 371-382.
  • [BD] V. M. Bondarenko and Yu. A. Drozd, The representation type of finite groups, in: Modules and Representations, Zap. Nauchn. Sem. LOMI 57 (1977), 24-41 (in Russian).
  • [Br1] S. Brenner, Large indecomposable modules over a ring of 2 × 2 triangular matrices, Bull. London Math. Soc. 3 (1971), 333-336.
  • [Br2] S. Brenner, On two questions of M. Auslander, ibid. 4 (1972), 301-302.
  • [DR] V. Dlab and C. M. Ringel, Indecomposable representations of graphs and algebras, Mem. Amer. Math. Soc. 173 (1976).
  • [DLS] P. Dowbor, H. Lenzing and A. Skowroński, Galois coverings of algebras by locally support-finite categories, in: Lecture Notes in Math. 1177, Springer, 1986, 41-93.
  • [DS1] P. Dowbor and A. Skowroński, On Galois coverings of tame algebras, Arch. Math. (Basel) 44 (1985), 522-529.
  • [DS2] P. Dowbor and A. Skowroński, On the representation type of locally bounded categories, Tsukuba J. Math. 10 (1986), 63-72.
  • [D] Yu. A. Drozd, On tame and wild matrix problems, in: Matrix Problems, Izdat. Inst. Mat. AN USSR, Kiev, 1977, 104-114.
  • [FGR] R. Fossum, Ph. Griffith and I. Reiten, Trivial Extensions of Abelian Categories, Lecture Notes in Math. 456, Springer, 1975.
  • [G1] P. Gabriel, Indecomposable representations I, Manuscripta Math. 6 (1972), 71-109.
  • [G2] P. Gabriel, Indecomposable representations II, Symposia Math. 11 (1973), 61-104.
  • [G3] P. Gabriel, Auslander-Reiten sequences and representation-finite algebras, in: Lecture Notes in Math. 831, Springer, 1980, 1-71.
  • [G4] P. Gabriel, The universal covering of a representation-finite algebra, in: Proc. Third Conf. on Representations of Algebras, Puebla, Lecture Notes in Math. 903, Springer, 1981, 68-105.
  • [HM] M. Hoshino and I. Miyachi, Tame triangular matrix algebras over self-injective algebras, Tsukuba J. Math. 11 (1987), 383-391.
  • [L1] Z. Leszczyński, l-hereditary triangular matrix algebras of tame type, Arch. Math. (Basel) 54 (1990), 25-31.
  • [L2] Z. Leszczyński, On the representation type of triangular matrix algebras over special algebras, Fund. Math. 137 (1991), 65-80.
  • [LS] Z. Leszczyński and D. Simson, On the triangular matrix rings of finite type, J. London Math. Soc. (2) 20 (1979), 396-402.
  • [LSk] Z. Leszczyński and A. Skowroński, Triangular matrix algebras of tame type, to appear.
  • [MS] H. Meltzer and A. Skowroński, Group algebras of finite representation type, Math. Z. 182 (1983), 129-148.
  • [R] C. M. Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer, 1984.
  • [S1] A. Skowroński, Group algebras of polynomial growth, Manuscripta Math. 59 (1987), 499-516.
  • [S2] A. Skowroński, Tame triangular matrix algebras over Nakayama algebras, J. London Math. Soc. 34 (1986), 245-264.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv144i2p143bwm
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