On the Auslander-Reiten Quiver with Oriented Cyclesof Representation-finite Algebras

数学季刊 ›› 1998, Vol. 13 ›› Issue (3): 43-47.

On the Auslander-Reiten Quiver with Oriented Cyclesof Representation-finite Algebras

Department of Mathematics,Beijing Polytechnic University,Beijing,100022

收稿日期:1997-01-08 出版日期:1998-09-30 发布日期:2024-10-23
基金资助:
Supported by China Postdoctoral Fund and Beijing Youth Fund．

On the Auslander-Reiten Quiver with Oriented Cyclesof Representation-finite Algebras

Department of Mathematics,Beijing Polytechnic University,Beijing,100022

Received:1997-01-08 Online:1998-09-30 Published:2024-10-23
Supported by:
Supported by China Postdoctoral Fund and Beijing Youth Fund．

摘要/Abstract

摘要： Let A be a basic,connected finite dimensional algebra over an algebraically closed field with finite representation type, α(A) be the maximum of set consisting of numbers of indecomposable summands in the middle term of Auslander Reiten sequences in mod A. In this paper we show that if α(A)=1, then Γ A contains oriented cycles if and only if Γ A contains DT r periodic modules. When α(A) we give counterexamples to the assertion.

关键词: Auslander-Reiten quiver, Auslander-Reiten sequences, oriented cycles, DT-r periodic molules

Abstract: Let A be a basic,connected finite dimensional algebra over an algebraically closed field with finite representation type, α(A) be the maximum of set consisting of numbers of indecomposable summands in the middle term of Auslander Reiten sequences in mod A. In this paper we show that if α(A)=1, then Γ A contains oriented cycles if and only if Γ A contains DT r periodic modules. When α(A) we give counterexamples to the assertion.

Key words: Auslander-Reiten quiver, Auslander-Reiten sequences, oriented cycles, DT-r periodic molules

中图分类号:

O153

姚海楼. On the Auslander-Reiten Quiver with Oriented Cyclesof Representation-finite Algebras[J]. 数学季刊, 1998, 13(3): 43-47.

Yao Hailou. On the Auslander-Reiten Quiver with Oriented Cyclesof Representation-finite Algebras[J]. Chinese Quarterly Journal of Mathematics, 1998, 13(3): 43-47.

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On the Auslander-Reiten Quiver with Oriented Cyclesof Representation-finite Algebras

On the Auslander-Reiten Quiver with Oriented Cyclesof Representation-finite Algebras

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