Quantum Groups and Noncommutative Geometry

Details Quantum Groups and Noncommutative Geometry Quantum Groups and Noncommutative Geometry

2000-06-21

arxiv.org/abs/hep-th/0006167v1

J.Math.Phys.41:3892-3942,2000

Physics

High Energy Physics

High Energy Physics - Theory

72 pages, many figures; intended for wider theoretical physics community (special millenium volume of JMP)

Scientific paper

10.1063/1.533331

Quantum groups emerged in the latter quarter of the 20th century as, on the one hand, a deep and natural generalisation of symmetry groups for certain integrable systems, and on the other as part of a generalisation of geometry itself powerful enough to make sense in the quantum domain. Just as the last century saw the birth of classical geometry, so the present century sees at its end the birth of this quantum or noncommutative geometry, both as an elegant mathematical reality and in the form of the first theoretical predictions for Planck-scale physics via ongoing astronomical measurements. Noncommutativity of spacetime, in particular, amounts to a postulated new force or physical effect called cogravity.

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