Quantum groups and noncommutative geometry
Quantum groups and noncommutative geometry
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DOI：
10.1063/1.533331
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发表时间：
2000-05
影响因子：
1.3
通讯作者：
S. Majid
中科院分区：
文献类型：
--
作者：
S. Majid
量子群出现在世纪的后25年，一方面是对某些可积系统的对称群的深刻而自然的推广，另一方面是对几何本身的推广的一部分，这种推广足够强大，在量子领域有意义。正如上个世纪见证了经典几何学的诞生，本世纪也见证了量子几何学或非对易几何学的诞生。量子几何学或非对易几何学既是一种优雅的数学现实，也是通过不断进行的天文测量对普朗克尺度物理学进行的第一次理论预测。特别是时空的非对易性，相当于一种新的假设力或物理效应，称为余引力。
Quantum groups emerged in the latter quarter of the 20th century as, on the one hand, a deep and natural generalization of symmetry groups for certain integrable systems, and on the other as part of a generalization 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 space–time, in particular, amounts to a postulated new force or physical effect called cogravity.