路代数和路余代数弱entwining结构的Hochschild上同调

The Hochschild Cohomology of the Weak Entwining Structure of a Path Algebra and a Path Coalgebra

为了研究弱entwining结构的性质,利用同调代数方法讨论了路代数和路余代数的弱entwining结构,研究了此弱entwining结构的Hochschild上同调及其性质,得到了此弱entwining结构中的路余代数所在基础图为树的等价条件.

In order to investigate the properties of weak entwining structures, in this paper we firstly use the methods of homological algebra to discuss the weak entwining structure of a path algebra and a path co-algebra, and then we research the Hochschild cohomology of the weak entwining structure and its properties, and obtain equivalent conditions that the underlying graph of the path coalgebra in such a weak entwining structure is a tree.