Noncommutative Geometry - Examples of Noncommutative Spaces

Examples of Noncommutative Spaces

  • In Weyl quantization, the symplectic phase space of classical mechanics is deformed into a non-commutative phase space generated by the position and momentum operators.
  • The standard model of particle physics is another example of a noncommutative geometry, cf noncommutative standard model.
  • 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
  • Noncommutative algebras arising from foliations.
  • Examples related to dynamical systems arising from number theory, such as the Gauss shift on continued fractions, give rise to noncommutative algebras that appear to have interesting noncommutative geometries.

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