Isomorphism problems of noncommutative deformations of type 𝐷 Kleinian singularities

Levy, Paul

doi:10.1090/S0002-9947-08-04593-5

Isomorphism problems of noncommutative deformations of type $D$ Kleinian singularities
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by Paul Levy PDF

Trans. Amer. Math. Soc. 361 (2009), 2351-2375 Request permission

Abstract:

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 isomorphism problem for the associative algebras thus constructed. We prove that (in our parametrization) all isomorphisms arise from the action of the normalizer $N_{\operatorname {SL}(2)}(\Gamma )$ 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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