Semi-classical differential structures
| dc.creator | Beggs, E. J. | |
| dc.creator | Majid, S. | |
| dc.date | 2003-06-18 | |
| dc.date | 2005-11-15 | |
| dc.date.accessioned | 2026-07-07T06:35:40Z | |
| dc.date.available | 2026-07-07T06:35:40Z | |
| dc.description | We semiclassicalise the standard notion of differential calculus in noncommutative geometry on algebras and quantum groups. We show in the symplectic case that the infinitesimal data for a differential calculus is a symplectic connection, and interpret its curvature as lowest order nonassociativity of the exterior algebra. Semiclassicalisation of the noncommutative torus provides an example with zero curvature. In the Poisson-Lie group case we study left-covariant infinitesimal data in terms of partially defined preconnections. We show that the moduli space of bicovariant infinitesimal data for quasitriangular Poisson-Lie groups has a canonical reference point which is flat in the triangular case. Using a theorem of Kostant, we completely determine the moduli space when the Lie algebra is simple: the canonical preconnection is the unique point for other than sl_n, n>2, when the moduli space is 1-dimensional. We relate the canonical preconnection to Drinfeld twists and thereby quantise it to a super coquasi-Hopf exterior algebra. We also discuss links with Fedosov quantisation. | |
| dc.description | 34 pages AMS-LATEX, no figures. Final version, as to be published. Note added with prior reference and notational changes `partial' -->`pre' only | |
| dc.identifier | https://arxiv.org/abs/math/0306273 | |
| dc.identifier | http://arxiv.org/abs/math/0306273 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99861 | |
| dc.subject | Quantum Algebra | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Symplectic Geometry | |
| dc.title | Semi-classical differential structures | |
| dc.type | text |