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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

   
 

 

Brauer's generalized decomposition numbers and universal deformation rings


Author: Frauke M. Bleher
Journal: Trans. Amer. Math. Soc. 366 (2014), 6507-6540
MSC (2010): Primary 20C20; Secondary 20C15, 16G10
DOI: https://doi.org/10.1090/S0002-9947-2014-06120-5
Published electronically: July 25, 2014
MathSciNet review: 3267017
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Abstract: The versal deformation ring $ R(G,V)$ of a mod $ p$ representation $ V$ of a profinite group $ G$ encodes all isomorphism classes of lifts of $ V$ to representations of $ G$ over complete local commutative Noetherian rings. We introduce a new technique for determining $ R(G,V)$ when $ G$ is finite which involves Brauer's generalized decomposition numbers.


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Additional Information

Frauke M. Bleher
Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242-1419
Email: frauke-bleher@uiowa.edu

DOI: https://doi.org/10.1090/S0002-9947-2014-06120-5
Keywords: Universal deformation rings, Brauer's generalized decomposition numbers, tame blocks, dihedral defect groups, semidihedral defect groups, generalized quaternion defect groups
Received by editor(s): December 3, 2012
Received by editor(s) in revised form: January 27, 2013
Published electronically: July 25, 2014
Additional Notes: The author was supported in part by NSA Grant H98230-11-1-0131.
Article copyright: © Copyright 2014 Frauke M. Bleher