赋值Hammocks

Hammock of the Valued Graphs

定义了赋值Hammock ,并证明如下两个定理 :(1)设A是Dynkin型赋值路代数 ,P(i)是不可分解投射A 模 ,则代数A的AR 箭图ΓA 中自然出现一个新的赋值HammockH(P(i) ) ;(2 )设H是赋值Hammock ,p是H的thin投射点 ,则 :Hp ={x∈H｜Homk(H) (p,x) ≠ 0 }和H/Hp ={x∈H｜hH(x) -h(Hp) (x) ≠ 0 }是赋值Hammock ,其Hammock函数分别为h(Hp) (- ) =dimHomk(H) (p,- )和h(H/Hp) =hH-h(Hp) .

Let A be a valued path algebra of Dynkin type, P(i) be an indecomposable projective A-module, we show that there is a new Hammock H(P(i)) of the AR-quiver of the algebra A; let H be a valued Hammock and p be a thin projective vertex of H that is different from the source,we prove that H p={x∈H|Hom k(H)(p,x)≠0}and H/H p={x∈H|h H(x)-h (H p)(x)≠0}are valued Hammocks.