COHOMOLOGY OF SPLIT ALGEBRAS AND OF TRIVIAL EXTENSIONS
COHOMOLOGY OF SPLIT ALGEBRAS AND OF TRIVIAL EXTENSIONS
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DOI：
10.1017/s0017089502008959
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发表时间：
2001-02
影响因子：
0.5
通讯作者：
Claude Cibils;E. Marcos;M. J. Redondo;A. Solotar
中科院分区：
文献类型：
--
作者：
Claude Cibils;E. Marcos;M. J. Redondo;A. Solotar
我们考虑具有双边理想$M$和子代数$A$直和分解的域上的结合代数$\Lambda$-例子是由平凡扩张或三角型矩阵代数提供的。在这个相对的和可分的背景下，我们描述了一个计算$\Lambda$的Hochschild上同调的长正合序列。我们利用杯积研究了连通同态，得到了几个结果，特别是平凡扩张的第一个Hochschild上同调群永远不会消失。
We consider associative algebras $\Lambda$ over a field provided with a direct sum decomposition of a two-sided ideal $M$ and a sub-algebra $A$ – examples are provided by trivial extensions or triangular type matrix algebras. In this relative and split setting we describe a long exact sequence computing the Hochschild cohomology of $\Lambda$. We study the connecting homomorphism using the cup-product and we infer several results, in particular the first Hochschild cohomology group of a trivial extension never vanishes.