Universal deformation rings and dihedral defect groups

Abstract

Let k be an algebraically closed field of characteristic 2, and let W be the ring of infinite Witt vectors over k. Suppose G is a finite group, and B is a block of kG with dihedral defect group D which is Morita equivalent to the principal 2-modular block of a finite simple group. We determine the universal deformation ring R(G,V) for every kG-module V which belongs to B and has stable endomorphism ring k. It follows that R(G,V) is always isomorphic to a subquotient ring of WD. Moreover, we obtain an infinite series of examples of universal deformation rings which are not complete intersections.

37 pages, 13 figures. Changed introduction, updated references

Cited by in corpus (2)

• Witt vectors. Part 1
• Universal deformation rings and dihedral 2-groups