l-遗传代数的Hochschild上同调群

设 $\Lambda$ 是域$k$上的有限维代数. 则 $\Lambda$的低阶 Hochschild上同调群在有限维代数的表示理论中扮演着重要的角色. 该文得到了 $l$ -遗传代数的一阶和二阶Hochschild 上同调群的维数方程.

Hochschild Cohomology of l-hereditary Algebras

Let $\Lambda$ be a finite-dimensional $k$-algebra over a field $k$. The low dimensional Hochschild cohomological groups $H^i(\Lambda)~(i \leq 2)$ have a classical interpretation and play an important role in representation theoryof finite-dimensional algebras. In this note the formulae on the dimensions of the first and the second Hochschild cohomology groups of $l$-hereditary algebras are obtained explicitly.