路代数的同构

ISOMORPHISMS OF PATH ALGEBRAS

设K(Δ)表示有向图Δ在域K上的路代数,本文证明:(1)K(Δ)^+与K(Γ)^+代数同构当且仅当Δ与Γ边同构。(2)K(Δ)与K(Γ)代数同构当且仅当Δ与Γ同构。

Let K(Δ)denote the path algebra of a quiver Δ over a field K. It is proved that: (1)K(Δ)^+ is isomorphic to K(Γ)^+ as K-algebras if and only if Δ and Γ are edge-isomorphic. (2) K(Δ)≈K(Γ)as K-algebras if and only ifΔ■ Γ as quivers.