科研之友
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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[a"currency sign/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.
- 出版日期2010-6
