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ISSN 1088-6850(e) ISSN 0002-9947(p)

Isomorphism problems of noncommutative deformations of type Kleinian singularities

Author(s): Paul Levy
Journal: Trans. Amer. Math. Soc. 361 (2009), 2351-2375.
MSC (2000): Primary 16S80, 16S38
Posted: December 23, 2008
MathSciNet review: 2471922
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Abstract: We construct all possible noncommutative deformations of a Kleinian singularity ${\mathbb{C}}^2/\Gamma$ of type 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 is isomorphic to a vector space of dimension .

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