Isomorphism Problems of Noncommutative Deformations of Type D Kleinian Singularities

Details Isomorphism Problems of Noncommutative Deformations of Type D Kleinian Singularities Isomorphism Problems of Noncommutative Deformations of Type D Kleinian Singularities

2006-10-16

arxiv.org/abs/math/0610490v1

Mathematics

Rings and Algebras

24 pages

Scientific paper

We construct all possible noncommutative deformations of a Kleinian singularity ${\mathbb C}^2/\Gamma$ of type $D_n$ in terms of generators and relations, and solve the problem of when two deformations are isomorphic. We prove that all isomorphisms arise naturally from the action of the normalizer $N_{\SL(2)}(\Gamma)$ on ${\mathbb C}/\Gamma$. We deduce that the moduli space of isomorphism classes of noncommutative deformations in type $D_n$ is isomorphic to a vector space of dimension $n$.

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