D_n型路代数倾斜模与AR箭图边缘

Modules over Path Algebras of Type D_n and Edges of AR-quivers

代数表示理论是上个世纪七十年代初兴起的代数学的一个新的分支,而倾斜理论是研究代数表示理论的重要工具之一.本文主要对D_n型路代数倾斜模在其对应的AR-箭图上的结构特点进行研究.通过对D_n型路代数A的AR-箭图Γ_A分析,证明了:D_n型路代数倾斜模T的一个必要条件是,〈T〉中至少有三个边缘点.

Representation theory of algebras is a new branch of algebra which began at the seventies of the last century. Tilting theory is an important tool to study representation theory of algebras. The main purpose of this paper is to study structural characteristics of the tilting module over path algebras of type Dn in theirs AR-quivers. It takes advantages of AR-quiver analysis. The paper shows that if T is a tilting A-module over a path algebra of type Dn, then there are at least three points corresponding indecomposable direct summands of T in the edges of ΓA.