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. ISSN 1088-6850

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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:
Journal 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
Uncontrolled Keywords:
/dk/atira/pure/core/keywords/mathsandstatistics/algebra
Subjects:
?? algebrageneral mathematicsmathematics(all) ??
ID Code:
51958
Deposited By:
Deposited On:
09 Dec 2011 13:32
Refereed?:
Yes
Published?:
Published
Last Modified:
16 Jul 2024 08:59