Journal article
Universal deformation rings and dihedral blocks with two simple modules
Journal of algebra, Vol.345(1), pp.49-71
12/07/2010
DOI: 10.1016/j.jalgebra.2011.08.010
Abstract
J. Algebra 345 (2011), 49-71 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 a dihedral defect group D such that there are precisely two isomorphism classes of simple B-modules. We determine the universal deformation ring R(G,V) for every finitely generated kG-module V which belongs to B and whose stable endomorphism ring is isomorphic to k. The description by Erdmann of the quiver and relations of the basic algebra of B is usually only determined up to a certain parameter c which is either 0 or 1. We show that R(G,V) is isomorphic to a subquotient ring of WD for all V as above if and only if c=0, giving an answer to a question raised by the first author and Chinburg in this case. Moreover, we prove that c=0 if and only if B is Morita equivalent to a principal block.
Details
- Title: Subtitle
- Universal deformation rings and dihedral blocks with two simple modules
- Creators
- Frauke M BleherGiovanna LlosentJennifer B Schaefer
- Resource Type
- Journal article
- Publication Details
- Journal of algebra, Vol.345(1), pp.49-71
- DOI
- 10.1016/j.jalgebra.2011.08.010
- ISSN
- 0021-8693
- eISSN
- 1090-266X
- Language
- English
- Date published
- 12/07/2010
- Academic Unit
- Mathematics
- Record Identifier
- 9983985969802771
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