Noncommutative Deformations of Type-A Kleinian Singularities

✍ Scribed by T.J. Hodges

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 717 KB
• Volume: 161
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1993.1219

✦ Synopsis

The type- (A) Kleinian singularities are the surfaces of the form (C^{2} / G) where (G) is a finite cyclic subgroup of (S L_{2}(\mathbb{C})). The standard noncommutative analog is the fixed ring of the Weyl algebra (A_{1}(\mathbb{C})) under the induced action of (G). These fixed rings are, however, only part of a large family of algebras whose associated graded ring is the coordinate ring of such a singularity. The structure of these algebras is studied with reference to the structure of the associated singularity and to the structure of primitive factor rings of (U(\mathbf{s i}(2, \mathbb{C}))). C 1993 Academic Press, Inc.