对称群S_4的泛变形环
Universal deformation rings for the symmetric group S_4
摘要：
设k是特征为2的代数闭域，W是k上的无穷Witt向量环.设S_4表示4个字母的对称群。对每个kS_4-模V确定了具有稳定自同态环k的泛变形环R（S_4，V），并证明了R（S_4，V）同构于k，同构于W[t]/（t^2，2 t），同构于群环W[Z/2].这给出了一个积极的答案，在这种情况下提出的一个问题的第一作者和Chinburg是否普遍变形环的代表有限群与稳定的自同态环k总是同构的一个subquotient环的群环超过W的缺陷群的模块块相关联的代表。
英文摘要：
Let k be an algebraically closed field of characteristic 2, and let W be the ring of infinite Witt vectors over k. Let S_4 denote the symmetric group on 4 letters. We determine the universal deformation ring R(S_4,V) for every kS_4-module V which has stable endomorphism ring k and show that R(S_4,V) is isomorphic to either k, or W[t]/(t^2,2t), or the group ring W[Z/2]. This gives a positive answer in this case to a question raised by the first author and Chinburg whether the universal deformation ring of a representation of a finite group with stable endomorphism ring k is always isomorphic to a subquotient ring of the group ring over W of a defect group of the modular block associated to the representation.
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