Algebraic Noncommutative Geometry
| dc.creator | Gratus, Jonathan | |
| dc.date | 1999-05-29 | |
| dc.date.accessioned | 2026-07-07T05:29:17Z | |
| dc.date.available | 2026-07-07T05:29:17Z | |
| dc.description | A noncommutative algebra $A$, called an algebraic noncommutative geometry, is defined, with a parameter $ε$ in the centre. When $ε$ is set to zero, the commutative algebra $A^0$ of algebraic functions on an algebraic manifold $M$ is obtained. This $A^0$ is a subalgebra of $C(M)$, which is dense if $M$ is compact. The generators of $A$ define an immersion of $M$ into $R^n$, and $M$ inherits a Poisson structure as the limit of the commutator. Thus $A$ is a quantisation of a Poisson manifold. If an ordering convention is prescribed for $A$ then a star product on $M$ is obtained. Homomorphism and isomorphisms between noncommutative geometries are defined, and the map from $A$ to the Heisenberg algebra is used both to give an analogue of a coordinate chart, and to give $A$ a quantum group structure. Examples of algebraic noncommutative geometries are given, which include $R^n$, $T^\star S^2$, $T^2$, $S^2$ and surfaces of rotation. A definition of a metric on $M$ which can be extended to noncommutative geometry is given and this is used in an application of noncommutative geometry to the numerical analysis of surfaces. | |
| dc.description | Latex 29 pages, no figures, submitted to Comm. Math. Physics | |
| dc.identifier | https://arxiv.org/abs/math/9905187 | |
| dc.identifier | http://arxiv.org/abs/math/9905187 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78580 | |
| dc.subject | Quantum Algebra | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | 81S05; 14A22; 81Q20; 58Z05 | |
| dc.title | Algebraic Noncommutative Geometry | |
| dc.type | text |