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Isomorphism problems of noncommutative deformations of type $D$ Kleinian singularities

Levy, Paul (2009) Isomorphism problems of noncommutative deformations of type $D$ Kleinian singularities. Transactions of the American Mathematical Society, 361. pp. 2351-2375.

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    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 $n$.

    Item Type: Article
    Journal or Publication Title: Transactions of the American Mathematical Society
    Additional Information: First published in Trans. Amer. Math. Soc. 361 (2009), published by the American Mathematical Society
    Subjects: UNSPECIFIED
    Departments: Faculty of Science and Technology > Mathematics and Statistics
    ID Code: 51958
    Deposited By: ep_importer_pure
    Deposited On: 09 Dec 2011 13:32
    Refereed?: Yes
    Published?: Published
    Last Modified: 09 Apr 2014 22:56
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/51958

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