Zn分次代数的Hochschild上同调群

摘要

In this note the definition of Hochschild cohomology groups of Zn-graded algebras is given, and the low dimensional Hochschild cohomology groups are described. Moreover, a necessary and sufficient condition for a Zn-graded algebra to be a graded separable algebra is given in terms of the first Hochschild cohomology group, and the one-to-one correspondence between the zero degree component of the second Hochschild cohomology group and the Hochschild extensions of A is obtained.%本文给出了Zn分次代数A的Hochschild上同调群的定义，对低阶Hochschild上同调群进行了刻画．利用第一阶Hochschild上同调群给出了Zn分次代数为分次可分代数的充要条件，证明了第二阶Hochschild上同调群的零次分支与A的Hochschild扩张之间的一一对应关系．