Preprojective algebras, differential operators and a Conze embedding for deformations of Kleinian singularities
Preprojective algebras, differential operators and a Conze embedding for deformations of Kleinian singularities
复制标题
DOI：
10.1007/s000140050105
复制
发表时间：
1999-11
影响因子：
0.9
通讯作者：
W. Crawley-Boevey
中科院分区：
文献类型：
--
作者：
W. Crawley-Boevey
对于域上的任何关联代数，我们定义一个代数族。对于颤振的路径代数，可以恢复M. P. Holland和作者引入的变形预投影代数。对于光滑曲线的坐标环，族包括a的微分算子环和SpecA的余切束的坐标环。在拟自由和有限生成a - a -双模的情况下，证明了它在局部化下的良好行为。我们用它证明了Kleinian奇点变形的Conze嵌入。
For any associative algebraAover a fieldKwe define a family of algebrasfor. In caseAis the path algebra of a quiver, one recovers the deformed preprojective algebra introduced by M. P. Holland and the author. In caseAis the coordinate ring of a smooth curve, the family includes the ring of differential operators forAand the coordinate ring of the cotangent bundle for SpecA. In caseAis quasi-free andAis a finitely generatedA-A-bimodule we prove thatis well-behaved under localization. We use this to prove a Conze embedding for deformations of Kleinian singularities.