Journal article
Universal deformation rings for the symmetric group S_4
Algebras and representation theory, Vol.13(3), pp.255-270
12/12/2008
DOI: 10.1007/s10468-008-9120-7
Abstract
Algebr. Represent. Theory 13 (2010), no. 3, 255-270. 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.
Details
- Title: Subtitle
- Universal deformation rings for the symmetric group S_4
- Creators
- Frauke M BleherGiovanna Llosent
- Resource Type
- Journal article
- Publication Details
- Algebras and representation theory, Vol.13(3), pp.255-270
- DOI
- 10.1007/s10468-008-9120-7
- ISSN
- 1386-923X
- eISSN
- 1572-9079
- Language
- English
- Date published
- 12/12/2008
- Academic Unit
- Mathematics
- Record Identifier
- 9983985951102771
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