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Universal deformation rings and dihedral 2-groups
Journal article   Peer reviewed

Universal deformation rings and dihedral 2-groups

Frauke M Bleher
Journal of the London Mathematical Society, Vol.79(1), pp.225-237
2009
DOI: 10.1112/jlms/jdn071
url
https://arxiv.org/pdf/0705.0834View
Open Access

Abstract

Let k be an algebraically closed field of characteristic 2, and let W be the ring of infinite Witt vectors over k . Suppose that D is a dihedral 2‐group. We prove that the universal deformation ring R ( D, V ) of an endo‐trivial kD ‐module V is always isomorphic to W [ℤ/2×ℤ/2]. As a consequence, we obtain a similar result for modules V with stable endomorphism ring k belonging to an arbitrary nilpotent block with defect group D . This confirms, for such V , conjectures on the ring structure of the universal deformation ring of V that had previously been shown for V belonging to cyclic blocks or to blocks with Klein four defect groups.

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