Automorphisms and Ideals of the Weyl Algebra
| dc.creator | Berest, Yuri | |
| dc.creator | Wilson, George | |
| dc.date | 2001-02-25 | |
| dc.date.accessioned | 2026-07-07T04:40:21Z | |
| dc.date.available | 2026-07-07T04:40:21Z | |
| dc.description | Let $A_1$ be the (first) Weyl algebra, and let $G$ be its automorphism group. We study the natural action of $G$ on the space of isomorphism classes of right ideals of $A_1$ (equivalently, of finitely generated rank 1 torsion-free right $A_1$-modules). We show that this space breaks up into a countable number of orbits each of which is a finite dimensional algebraic variety. Our results are strikingly similar to those for the commutative algebra of polynomials in two variables; however, we do not know of any general principle that would allow us to predict this in advance. As a key step in the proof, we obtain a new description of the bispectral involution of \cite{W1}. We also make some comments on the group $G$ from the viewpoint of Shafaravich's theory of infinite dimensional algebraic groups. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/math/0102190 | |
| dc.identifier | http://arxiv.org/abs/math/0102190 | |
| dc.identifier | Math. Ann. 318, 127-147 (2000) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61000 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.title | Automorphisms and Ideals of the Weyl Algebra | |
| dc.type | text |