Universal deformation rings and generalized quaternion defect groups
Group Theory
2010-09-16 v2
Abstract
We determine the universal deformation ring R(G,V) of certain mod 2 representations V of a finite group G which belong to a 2-modular block of G whose defect groups are isomorphic to a generalized quaternion group D. We show that for these V, a question raised by the author and Chinburg concerning the relation of R(G,V) to D has an affirmative answer. We also show that R(G,V) is a complete intersection even though R(G/N,V) need not be for certain normal subgroups N of G which act trivially on V.
Cite
@article{arxiv.0909.1031,
title = {Universal deformation rings and generalized quaternion defect groups},
author = {Frauke M. Bleher},
journal= {arXiv preprint arXiv:0909.1031},
year = {2010}
}
Comments
20 pages, 6 figures. The paper has been updated as follows: The results remain true for more general 2-modular blocks with generalized quaternion defect groups (see the introduction and Hypothesis 3.1). Sections 4 and 5 have been swapped.