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

Research output: Contribution to journalJournal article

Published

Journal publication date2009
JournalTransactions of the American Mathematical Society
Volume361
Number of pages25
Pages2351-2375
Original languageEnglish

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 $n$.

Bibliographic note

First published in Trans. Amer. Math. Soc. 361 (2009), published by the American Mathematical Society