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。
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。
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。
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。
By using two kinds of affine representations of lie color algebras and the first cohomology group , we obtain some necessary or sufficient conditions to the problem whether there is any left color sysmmetric structure on a given lie color algebra which generalize the result of [ 2 ] 利用着色李超代数的两种仿射表示和1 -上同调群，得出左着色对称结构存在的几个充分或必要条件，推广了文[ 2 ]的结论。
