| 1. | The investigation of hochschild cohomology and homology originated from the literature by g . hochschild in 1945
代数的hochschild同调和上同调的研究始于g . hochschild于1945年的文献。 |
| 2. | The relationship of simple connectedness and 1 hochschild cohomology group is very clear for representation - finite algebras
单连通性和一次hochschild上同调群之间的联系，在有限表示型的情形已经很清楚了。 |
| 3. | Especially , we compute the hochschild cohomology of endomorphism algebras of complete exceptional sequence of the path algebra whose quiver has 3 vertices and has no orientation
第四章中，我们主要研究具有三个点的且不带方向圈的有向箭图的路代数上的完备例外序列的自同态代数的hochschild上同调群。 |
| 4. | In chapter 3 , we study the property of complete exceptional sequence . in chapter 4 , we make research on the hochschild cohomology of endomorphism algebras of complete exceptional sequence over hereditary algebras
第三章，我们证明了有限维遗传代数中，完备例外序列的维数向量的性质定理以及完备例外序列的诚实性。 |
| 5. | Lower degree hochschild cohomology group have a very concrete interpretation of classic algebraic structure , especially , there are inner connection between 1 hochschild cohomology group and simply connected algebra
低次的hochschild上同调群对于典型的代数的结构有具体的解释，尤其是一次的hochschild上同调群与单连通代数有着内在的联系。 |
| 6. | 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。 |
| 7. | The main conclusion is as follows : for i > 2 , the hochschild homology hi ( a ) of an algebra a is equal to the the hochschild homology hi ( b ) of the algebra b where b = a / j and j is a heredity ideal of a . c . cibils studied the hochschild cohomology of split algebras with bicom - plexs
本文中，我们首先就一类特殊的同调理想-遗传理想j进行了研究，给出了a和b在次数大于1时其hochschild同调相等的证明，对于其一次和0次hochschild同调可用一个正合列联系它们。 |
| 8. | 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。 |
