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单词 NoncommutativeGeometry
释义

noncommutative geometry


1 Topic on Non-commutative Geometry (NCG)

Noncommutative geometryPlanetmathPlanetmath utilizes non-AbelianPlanetmathPlanetmath (or nonabelianPlanetmathPlanetmath) methods for quantization of spaces through deformationMathworldPlanetmath to non-commutative ’spaces’ (in fact non-commutative algebraic structuresPlanetmathPlanetmath, or algebras of functions).

An alternative meaning is often given to noncommutative geometry (viz . A Connes et al.):that is, as a non-commutative ‘geometric’ approach– in the relativistic sense– to quantum gravity.

A specific example due to A. Connes is the convolution C*-algebraMathworldPlanetmath of (discrete) groups;other examples are non-commutative C*-algebras of operators defined on Hilbert spacesMathworldPlanetmath ofquantum operators and states.

1.1 Recent Developments in NCG

  • The Royal Swedish Academy of Sciences has awarded the 2001 Crafoord Prize in mathematicsto Professor Alain Connes of the Institut des Hautes Études Scientifiques (IHES) and theCollége de France, Paris, “for his penetrating work on the theory of… (quantum)… operator algebrasand for having been a founder of noncommutative geometry”.(http://www.ams.org/notices/200105/comm-crafoord.pdfCrafoord Prize in 2001 in Noncommutative Geometry and Quantum Operator AlgebrasPlanetmathPlanetmathPlanetmath).

    Professor Alain Connes is also the 1983 recipient of the Field Medal. The following is a concise quote of his workfrom the Crafoord Prize announcement in 2001: “Noncommutative geometry is a new field of mathematics, andConnes played a decisive role in its creation. His work has also provided powerful new methods for treating renormalization theory and the standard model of quantum and particle physics…(SUSY) (http://planetmath.org/SpinGroup)…He has demonstrated that these new mathematical tools can be used for understanding and attacking the Riemann Hypothesis.

  • The Crafoord Prize prize consisted of a gold medal and US dollars 500,000. The Anna-Greta and Holger Crafoord Foundation was established in 1980 for promoting basic research in mathematics, astronomy, the biosciences(particularly ecology), the geosciences, and polyarthritis (joint rheumatism)”. Previous (‘Nobel style’), CrafoordLaureates in Mathematics were: Vladimir I. Arnold and Louis Nirenberg in 1982, Alexandre Grothendieck (who publicly declined the prize) and Pierre Deligne–who accepted the prize in 1988, and Simon Donaldson and Shing-Tung Yau (1994).

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更新时间:2025/5/4 9:04:16