广义路代数的实现

A Presentation of Generalized Path Algebras

摘要: 设K为代数闭域,Δ=(Δ₀,Δ₁)为有限箭图,A=A_i|i∈Δ0为一集含单位元的有限维basic K-代数.通过构造箭图Γ,证明了广义路代数R(Δ,A)为路代数KΓ的商代数,并的到了一些有趣的推论.

Abstract: Suppose that K is algebraically closed,Δ=(Δ₀,Δ₁) a finite quiver,A=A_i|i∈Δ₀ a family of K-algebras with identity.In this note,by constructing a quiver Γ,we show that the generalized path algebra R(Δ,A) is the quotients of path algebra KΓ.Therefore,we get some interesting corollaries.