On the representation type of tensor product algebras

Zbigniew Leszczyński

Fundamenta Mathematicae (1994)

  • Volume: 144, Issue: 2, page 143-161
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Leszczyński, Zbigniew. "On the representation type of tensor product algebras." Fundamenta Mathematicae 144.2 (1994): 143-161. <http://eudml.org/doc/212020>.

@article{Leszczyński1994,
abstract = {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.},
author = {Leszczyński, Zbigniew},
journal = {Fundamenta Mathematicae},
keywords = {representation type of tensor product algebras; finite-dimensional basic connected -algebras; quivers with relations; algebra of lower triangular matrices; simply connected algebras; weakly sincere simply connected algebras; tame group algebras; tame triangular matrix algebras; Nakayama algebras},
language = {eng},
number = {2},
pages = {143-161},
title = {On the representation type of tensor product algebras},
url = {http://eudml.org/doc/212020},
volume = {144},
year = {1994},
}

TY - JOUR
AU - Leszczyński, Zbigniew
TI - On the representation type of tensor product algebras
JO - Fundamenta Mathematicae
PY - 1994
VL - 144
IS - 2
SP - 143
EP - 161
AB - 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.
LA - eng
KW - representation type of tensor product algebras; finite-dimensional basic connected -algebras; quivers with relations; algebra of lower triangular matrices; simply connected algebras; weakly sincere simply connected algebras; tame group algebras; tame triangular matrix algebras; Nakayama algebras
UR - http://eudml.org/doc/212020
ER -

References

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  3. [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). Zbl0429.16026
  4. [Br1] S. Brenner, Large indecomposable modules over a ring of 2 × 2 triangular matrices, Bull. London Math. Soc. 3 (1971), 333-336. Zbl0223.16012
  5. [Br2] S. Brenner, On two questions of M. Auslander, ibid. 4 (1972), 301-302. Zbl0261.16015
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  9. [DS2] P. Dowbor and A. Skowroński, On the representation type of locally bounded categories, Tsukuba J. Math. 10 (1986), 63-72. Zbl0604.16024
  10. [D] Yu. A. Drozd, On tame and wild matrix problems, in: Matrix Problems, Izdat. Inst. Mat. AN USSR, Kiev, 1977, 104-114. 
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  12. [G1] P. Gabriel, Indecomposable representations I, Manuscripta Math. 6 (1972), 71-109. 
  13. [G2] P. Gabriel, Indecomposable representations II, Symposia Math. 11 (1973), 61-104. 
  14. [G3] P. Gabriel, Auslander-Reiten sequences and representation-finite algebras, in: Lecture Notes in Math. 831, Springer, 1980, 1-71. 
  15. [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. 
  16. [HM] M. Hoshino and I. Miyachi, Tame triangular matrix algebras over self-injective algebras, Tsukuba J. Math. 11 (1987), 383-391. Zbl0639.16020
  17. [L1] Z. Leszczyński, l-hereditary triangular matrix algebras of tame type, Arch. Math. (Basel) 54 (1990), 25-31. 
  18. [L2] Z. Leszczyński, On the representation type of triangular matrix algebras over special algebras, Fund. Math. 137 (1991), 65-80. Zbl0727.16011
  19. [LS] Z. Leszczyński and D. Simson, On the triangular matrix rings of finite type, J. London Math. Soc. (2) 20 (1979), 396-402. Zbl0434.16022
  20. [LSk] Z. Leszczyński and A. Skowroński, Triangular matrix algebras of tame type, to appear. Zbl0978.16014
  21. [MS] H. Meltzer and A. Skowroński, Group algebras of finite representation type, Math. Z. 182 (1983), 129-148. Zbl0504.16006
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  24. [S2] A. Skowroński, Tame triangular matrix algebras over Nakayama algebras, J. London Math. Soc. 34 (1986), 245-264. Zbl0606.16021

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