As preparation, we first investigate the graded differential operators on a path algebra and the associated graded Lie algebra. Thirdly, we study the first cohomology of admissible algebras which can be seen as a generalization of basic algebras. 作为准备,我们首先讨论了路代数上的分次微分算子和相应的分次李代数。第三,我们研究了容许代数的一阶上同调,容许代数可以看做基本代数的推广。