Classifying blocks with abelian defect groups of rank 3 for the prime 2
Classifying blocks with abelian defect groups of rank 3 for the prime 2
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对素数 2 的具有 3 阶阿贝尔缺陷组的块进行分类
DOI：
10.1016/j.jalgebra.2018.08.010
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发表时间：
2017
影响因子：
0.9
通讯作者：
M. Livesey
中科院分区：
文献类型：
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作者：
Charles W. Eaton;M. Livesey
本文对所有亏群为C2n × C2 × C2的块进行分类，直到Morita等价.再加上最近的论文吴，张和周，这完成了分类的森田等价类的2块与阿贝尔亏损群的秩最多为3。分类持有块在一个合适的离散赋值环，以及那些在代数闭域。在本文中考虑的情况下是重要的，因为它涉及到比较森田等价类之间的一个组和一个正常的子群指数为2，所以需要新的减少技术，我们希望将更广泛的兴趣。我们注意到，这也完成了分类块阿贝尔缺陷组的顺序划分16森田等价。一个结果是，Broue的阿贝尔亏群猜想持有上述所有块。
In this paper we classify all blocks with defect group C 2 n× C 2× C 2 up to Morita equivalence. Together with a recent paper of Wu, Zhang and Zhou, this completes the classification of Morita equivalence classes of 2-blocks with abelian defect groups of rank at most 3. The classification holds for blocks over a suitable discrete valuation ring as well as for those over an algebraically closed field. The case considered in this paper is significant because it involves comparison of Morita equivalence classes between a group and a normal subgroup of index 2, so requires novel reduction techniques which we hope will be of wider interest. We note that this also completes the classification of blocks with abelian defect groups of order dividing 16 up to Morita equivalence. A consequence is that Broue's abelian defect group conjecture holds for all blocks mentioned above.
具有阿贝尔缺陷群的块的洛威长度
DOI：
10.1090/bproc/28
发表时间：
2017
期刊：
Proceedings of the American Mathematical Society, Series B
影响因子：
--
作者：
Eaton C
通讯作者：
Eaton C