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arXiv 0909.1031math.GR
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泛变形环与广义四元数亏群

Universal deformation rings and generalized quaternion defect groups

Frauke M. Bleher

备注：
20 pages, 6 figures. The paper has been updated as follows: The results remain true for more general 2-modular blocks with generalized quaternion defect groups (see the introduction and Hypothesis 3.1). Sections 4 and 5 have been swapped.
发表信息：
Adv. Math. 225 (2010), 1499-1522
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摘要：

确定了有限群G的模2表示V的泛变形环R（G，V），其中V属于G的2-模块，其亏群同构于广义四元数群D.我们表明，对于这些V，一个问题所提出的作者和Chinburg有关的关系R（G，V）的D有一个肯定的答案。我们还证明了R（G，V）是一个完全交，即使R（G/N，V）对于G的某些正规子群N对V作用平凡不一定是。

英文摘要：

We determine the universal deformation ring R(G,V) of certain mod 2 representations V of a finite group G which belong to a 2-modular block of G whose defect groups are isomorphic to a generalized quaternion group D. We show that for these V, a question raised by the author and Chinburg concerning the relation of R(G,V) to D has an affirmative answer. We also show that R(G,V) is a complete intersection even though R(G/N,V) need not be for certain normal subgroups N of G which act trivially on V.

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