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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Author: Paul Levy
Journal: Trans. Amer. Math. Soc. 361 (2009), 2351-2375
MSC (2000): Primary 16S80, 16S38
Published electronically: 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 $ 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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Additional Information

Paul Levy
Affiliation: Section Mathematics, Ecole Polytechnique Federal de Lausanne, Bâtiment BCH, CH-1015 Lausanne, Switzerland
Email: paul.levy@epfl.ch

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04593-5
PII: S 0002-9947(08)04593-5
Received by editor(s): March 21, 2007
Published electronically: December 23, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.