Abstract.
For any associative algebra A over a field K we define a family of algebras \( \Pi^\lambda(A) \) for \( \lambda \in K \,\otimes_{\Bbb Z}\,{\rm K_0}(A) \). In case A is the path algebra of a quiver, one recovers the deformed preprojective algebra introduced by M. P. Holland and the author. In case A is the coordinate ring of a smooth curve, the family includes the ring of differential operators for A and the coordinate ring of the cotangent bundle for Spec A. In case A is quasi-free and \( \Omega^1 \) A is a finitely generated A-A-bimodule we prove that \( \Pi^\lambda(A) \) is well-behaved under localization. We use this to prove a Conze embedding for deformations of Kleinian singularities.
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Received: March 4, 1998.
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Crawley-Boevey, W. Preprojective algebras, differential operators and a Conze embedding for deformations of Kleinian singularities. Comment. Math. Helv. 74, 548–574 (1999). https://doi.org/10.1007/s000140050105
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DOI: https://doi.org/10.1007/s000140050105