So , secondly , we constructed the one paremeter family of deformation of split algebras , we obtained the results from the method of c . cibils , not from the definition given by m . gerstenhaber . specially , we discussed the one parameter family of deformation of trivial algebras C . cibils从双复形的角度对分裂代数的hochschild上同调进行了研究，借助其方法，我们在文章的第二部分对分裂代数的形变理论做了研究。
The main content of this paper is the cohomologies and extensions over triangular hopf algebra . according to [ l ] , we consider the cohomologies and extensions and then the relationships between them in the category of the modules of triangular hopf algebra h . and the category is a symmetry monoidal category 论文主要考虑的内容是上同调与扩张，根据文献[ 1 ] ，具体的考虑作为对称的monoidal范畴的三角hopf代数h的模范畴的上同调与扩张及它们之间的关系。
E for an algebra of minimal representation - infinite type with preprojective component , it is simply connected if and only if the vanishing of 1 hochschild cohomology group ; the same conclusion is true for a general algebra with minimal representation - infinite type . in chapter 3 , we computed the fundamental group for hereditary algebra and other special cases , and studied the fundamental group under one point extension 在第二章中我们得到了极小无限表示型代数单连通性的一些结论：对于具有预投射分支的极小无限表示型代数，它是单连通当且仅当其一次hochschild上同调群为零；而对于一般情形的极小无限表示型代数，也是如此。第三章中，我们对基本群在遗传代数等几种特殊情况下，对于一些例子作了计算。
