Rights statement: First published in Trans. Amer. Math. Soc. 361 (2009), published by the American Mathematical Society
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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Isomorphism problems of noncommutative deformations of type $D$ Kleinian singularities
AU - Levy, Paul
N1 - First published in Trans. Amer. Math. Soc. 361 (2009), published by the American Mathematical Society
PY - 2009
Y1 - 2009
N2 - 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 $n$.
AB - 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 $n$.
U2 - 10.1090/S0002-9947-08-04593-5
DO - 10.1090/S0002-9947-08-04593-5
M3 - Journal article
VL - 361
SP - 2351
EP - 2375
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 1088-6850
ER -