By the means of multiplication of path algebras,Lie algebras are constructed naturally.In this paper,firstly,the center of Lie algebras constructed by acyclic path algebras are given.Then it is proved that there is a degree preserving Lie algebras isomorphism if the isomorphism of Lie algebras constructed by two acyclic quivers exists.Finally,the necessary and sufficient condition for the isomorphism of Lie algebras constructed by two alternating quivers is that they have the same number of vertexes and arrows.
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