Noncommutative Lattices and the Algebra of their Continuous Functions
| dc.creator | Ercolessi, Elisa | |
| dc.creator | Landi, Giovanni | |
| dc.creator | Teotonio-Sobrinho, Paulo | |
| dc.date | 1996-07-15 | |
| dc.date | 1996-07-17 | |
| dc.date.accessioned | 2026-07-07T09:08:40Z | |
| dc.date.available | 2026-07-07T09:08:40Z | |
| dc.description | Recently a new kind of approximation to continuum topological spaces has been introduced, the approximating spaces being partially ordered sets (posets) with a finite or at most a countable number of points. The partial order endows a poset with a nontrivial non-Hausdorff topology. Their ability to reproduce important topological information of the continuum has been the main motivation for their use in quantum physics. Posets are truly noncommutative spaces, or {\it noncommutative lattices}, since they can be realized as structure spaces of noncommutative $C^*$-algebras. These noncommutative algebras play the same role of the algebra of continuous functions ${\cal C}(M)$ on a Hausdorff topological space $M$ and can be thought of as algebras of operator valued functions on posets. In this article, we will review some mathematical results that establish a duality between finite posets and a certain class of C$^*$-algebras. We will see that the algebras in question are all postliminal approximately finite dimensional (AF) algebras. | |
| dc.description | 31 pages, latex | |
| dc.identifier | https://arxiv.org/abs/q-alg/9607016 | |
| dc.identifier | http://arxiv.org/abs/q-alg/9607016 | |
| dc.identifier | Rev.Math.Phys. 10 (1998) 439-466 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150802 | |
| dc.subject | Quantum Algebra | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Noncommutative Lattices and the Algebra of their Continuous Functions | |
| dc.type | text |