Abelian and non-abelian second cohomologies of quantized enveloping algebras
Abelian and non-abelian second cohomologies of quantized enveloping algebras
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DOI：
10.1016/j.jalgebra.2008.03.034
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发表时间：
2007-08
影响因子：
0.9
通讯作者：
A. Masuoka
中科院分区：
文献类型：
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作者：
A. Masuoka
对于一类包括量化包络代数在内的尖Hopf代数，我们讨论了裂扩张、余循环变形和第二上同调。我们提出了一种计算阿贝尔第二上同调的非标准方法，该方法从分类裂扩展的非阿贝尔第二上同调中导出信息。作为示例计算，证明了李代数上同调的怀特海第二引理的量子模拟。
For a class of pointed Hopf algebras including the quantized enveloping algebras, we discuss cleft extensions, cocycle deformations and the second cohomology. We present such a non-standard method of computing the abelian second cohomology that derives information from the non-abelian second cohomology classifying cleft extensions. As a sample computation, a quantum analogue of Whitehead's second lemma for Lie-algebra cohomology is proved.