Universal deformation rings and dihedral defect groups

Bleher, Frauke

doi:10.1090/S0002-9947-09-04543-7

Universal deformation rings and dihedral defect groups
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by Frauke M. Bleher PDF

Trans. Amer. Math. Soc. 361 (2009), 3661-3705 Request permission

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.

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