Hochschild cohomology and “smoothness” in monoidal categories
Hochschild cohomology and “smoothness” in monoidal categories
复制标题
DOI：
10.1016/j.jpaa.2005.12.003
复制
发表时间：
2007
影响因子：
0.8
通讯作者：
A. Ardizzoni;C. Menini;D. Ştefan
中科院分区：
文献类型：
--
作者：
A. Ardizzoni;C. Menini;D. Ştefan
引入并研究了交换么半范畴M中代数的Hochschild上同调群的性质，证明了M中代数的第二个Hochschild上同调群将A的扩张分类为等价的。刻划了Hochschild维0(可分代数)和Hochschild维≤1(形式光滑代数)的代数。文章的最后一节列举了几个具体的案例和应用。
We introduce and investigate the properties of Hochschild cohomology of algebras in an abelian monoidal category M. We show that the second Hochschild cohomology group of an algebra in M classifies extensions of A up to an equivalence. We characterize algebras of Hochschild dimension 0 (separable algebras), and of Hochschild dimension ≤1 (formally smooth algebras). Several particular cases and applications are included in the last section of the paper.