Hochschild cohomology and stratifying ideals
Hochschild cohomology and stratifying ideals
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DOI：
10.1016/j.jpaa.2008.10.012
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发表时间：
2009-05
影响因子：
0.8
通讯作者：
S. Koenig;H. Nagase
中科院分区：
文献类型：
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作者：
S. Koenig;H. Nagase
设B是一个代数，其分层理想Be B由幂等元e生成.我们将建立三个代数B，B/Be B和eBe的Hochschild上同调群之间的长正合序列.这提供了一个共同的推广各种已知的结果，所有这些扩展哈佩尔的长正合序列的一点扩展。应用这些序列之一，以Hochschild上同调代数模的理想所产生的齐次幂零元素表明，在某些情况下，这些代数是双生成的。
Suppose B is an algebra with a stratifying ideal BeB generated by an idempotent e. We will establish long exact sequences relating the Hochschild cohomology groups of the three algebras B, B/BeB and eBe. This provides a common generalization of various known results, all of which extend Happel’s long exact sequence for one-point extensions. Applying one of these sequences to Hochschild cohomology algebras modulo the ideal generated by homogeneous nilpotent elements shows, in some cases, that these algebras are finitely generated.