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...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)2 we give counterexamples to the assertion.展开更多
The representations of the Dynkin quivers and the corresponding Euclidean quivers are treated in many books. These notes provide three building blocks for dealing with representations of Dynkin （and Euclidean） quive...The representations of the Dynkin quivers and the corresponding Euclidean quivers are treated in many books. These notes provide three building blocks for dealing with representations of Dynkin （and Euclidean） quivers. They should be helpful as part of a direct approach to study representations of quivers, and they shed some new light on properties of Dynkin and Euclidean quivers.展开更多
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 ...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.展开更多
文摘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)2 we give counterexamples to the assertion.
文摘The representations of the Dynkin quivers and the corresponding Euclidean quivers are treated in many books. These notes provide three building blocks for dealing with representations of Dynkin （and Euclidean） quivers. They should be helpful as part of a direct approach to study representations of quivers, and they shed some new light on properties of Dynkin and Euclidean quivers.
文摘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.
