Editing Noncommutative geometry (section)

==Examples of noncommutative spaces==
* In the [[phase space formulation]] of quantum mechanics,  the [[Symplectic manifold|symplectic]] [[phase space]] of [[Hamiltonian mechanics|classical mechanics]] is [[deformation quantization|deformed]] into a non-commutative phase space generated by the [[Heisenberg group|position and momentum operators]].
* The [[noncommutative torus]], deformation of the function algebra of the ordinary torus, can be given the structure of a spectral triple. This class of examples has been studied intensively and still functions as a test case for more complicated situations.
* Snyder space<ref>{{cite journal | last=Snyder | first=Hartland S. | title=Quantized Space-Time | journal=[[Physical Review]] | publisher=American Physical Society (APS) | volume=71 | issue=1 | date=1947-01-01 | issn=0031-899X | doi=10.1103/physrev.71.38 | pages=38–41| bibcode=1947PhRv...71...38S }}</ref>
* Noncommutative algebras arising from [[foliation]]s.
* Examples related to [[dynamical systems]] arising from [[number theory]], such as the [[Continued fractions#Continued fractions and dynamical systems|Gauss shift]] on continued fractions, give rise to noncommutative algebras that appear to have interesting noncommutative geometries.