Ideal Classes of the Weyl Algebra and Noncommutative Projective Geometry (with an Appendix by M. Van den Bergh)
| dc.creator | Berest, Yuri | |
| dc.creator | Wilson, George | |
| dc.date | 2001-04-26 | |
| dc.date | 2001-08-08 | |
| dc.date.accessioned | 2026-07-07T04:41:28Z | |
| dc.date.available | 2026-07-07T04:41:28Z | |
| dc.description | Let R be the set of isomorphism classes of ideals in the Weyl algebra $A=A_{1}$, and let C be the set of isomorphism classes of triples (V; X, Y), where V is a finite-dimensional (complex) vector space, and X, Y are endomorphisms of V such that [X,Y]+I has rank 1. Following a suggestion of L. Le Bruyn, we define a map $θ: R \to C$ by appropriately extending an ideal of A to a sheaf over a quantum projective plane, and then using standard methods of homological algebra. We prove that $θ$ is inverse to a bijection $ω: C \to R$ constructed in \cite{BW} by a completely different method. The main step in the proof is to show that $θ$ is equivariant with respect to natural actions of the group G=Aut(A) on R and C: for that we have to study also the extensions of an ideal to certain weighted quantum projective planes. Along the way, we find an elementary description of θ. | |
| dc.description | 38 pages, an Appendix by M. Van den Bergh has been added; the labels in quiver diagrams have been fixed | |
| dc.identifier | https://arxiv.org/abs/math/0104248 | |
| dc.identifier | http://arxiv.org/abs/math/0104248 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61368 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Quantum Algebra | |
| dc.title | Ideal Classes of the Weyl Algebra and Noncommutative Projective Geometry (with an Appendix by M. Van den Bergh) | |
| dc.type | text |