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A Condition for a Translation Quiver to Be a Coil 被引量：1

A Condition for a Translation Quiver to Be a Coil
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摘要 We single out a class of translation quivers and prove combinatorially that the translation quivers in this class are coils. These coils form a class of special coils. They are easier to visualize, but still show all the strange behaviour of general coils, and contain quasi-stable tubes as special examples. We single out a class of translation quivers and prove combinatorially that the translation quivers in this class are coils. These coils form a class of special coils. They are easier to visualize, but still show all the strange behaviour of general coils, and contain quasi-stable tubes as special examples.
作者 BinZHU ZongYiHU
机构地区 CollegeofMathematics&Econometrics DepartmentofMathematicalSciences
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2003年第1期107-126,共20页 数学学报（英文版）
关键词 Translation quivers Auslander Reiten quivers Coils Length functions Translation quivers Auslander Reiten quivers Coils Length functions
分类号 O157.5 [理学—基础数学]
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参考文献14

  • 1Brenner, S.: A Combinatorial Characterization of Finite Auslander-Reiten Quiver. Lecture Notes in Math.,Springer-Verlag, 1177, 13-49 (1986).
  • 2D'Este, G., Ringel, C. M.: Coherent Tubes. J. Algebra, 87, 150-201 (1984).
  • 3Ringel, C. M.: Tame Algebras and Integral Quadratic Forms. Lecture Notes in Math., Springer-Verlag,1099, (1984).
  • 4Liu, S. P.: "Shapes of Connected Components of the Auslander-Reiten Quivers of Artin Algebras. In "Representation Theory of Algebras and Related Topics", CMS Conference Proceedings, 19, 109-137 (1996).
  • 5Assem, I., Skowrofiski, A.: Indecomposable Modules over Multicoil Algebras. Math. Scand, 71, 31-61(1992).
  • 6Assem, I., Skowrofiski, A.: Multicoil Algebras. In "Representation Theory of Algebras", CMS Conference Proceedings, 14, 29-68 (1993).
  • 7de la Pefia, J. A., Skowrofiski, A.: Geometric and Homological Characterizations of Polynomial Growth Strongly Connected Algebras. Invent. Math., 126(2), 287-296 (1996).
  • 8Skowronski, A.: Algebras of Polynomial Growth. In "Topics in Algebra", Banach Center Publications,Warszawa, 26, 535-568 (1990).
  • 9Skowronski, A.: Simply Connected Algebras of Polynomial Growth. Composition Math., 109, 99-133(1997).
  • 10Agoston, I., Lukacs, E., Ringel, C. M.: Frobenius Functions on Translation Quivers. In "Representation Theory of Algebras", CMS Conference Proceedings, 18, 17-37 (1996).

引证文献1

Acta Mathematica Sinica,English Series
2003年 第1期

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