Noncommutative geometry based on commutator expansions
| dc.creator | Kapranov, Mikhail | |
| dc.date | 1998-02-07 | |
| dc.date.accessioned | 2026-07-07T05:23:48Z | |
| dc.date.available | 2026-07-07T05:23:48Z | |
| dc.description | We develop an approach to noncommutative algebraic geometry ``in the perturbative regime" around ordinary commutative geometry. Let R be a noncommutative algebra and A=R/[R,R] its commutativization. We describe what should be the formal neighborhood of M=Spec(A) in the (nonexistent) space Spec(R). This is a ringed space (M,O) where O is a certain sheaf of noncommutative rings on M. Such ringed spaces can be glued together to form more global objects called NC-schemes. We are especially interested in NC-manifolds, NC-schemes for which the completion of O at every point of M is isomorphic to the algebra of noncommutative power series (completion of the free associative algebra). An explicit description of the simplest NC-manifold, the affine space, is given by using the Feynman-Maslov calculus of ordered operators. We show that many familiar algebraic varieties can be naturally enlarged to NC-manifolds. Among these are all the classical flag varieties and all the smooth moduli spaces of vector bundles. | |
| dc.description | plain TEX, 48 pages | |
| dc.identifier | https://arxiv.org/abs/math/9802041 | |
| dc.identifier | http://arxiv.org/abs/math/9802041 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76587 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Noncommutative geometry based on commutator expansions | |
| dc.type | text |