Erlangen Programme

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The view, put forward by the German mathematician Felix Klein (1849–1925) in 1872 when he became a faculty member of the University of Erlangen, that each type of geometry can be characterized by a group of transformations. There are many physical examples of this including the Lorentz group of Minkowski space–time and the space groups of crystals. However, not all types of geometry fit into this view readily; in particular, Riemannian geometry, and hence curved space–time, do not fit unless the Erlangen Programme is given a wider interpretation. It has been suggested that such a broader interpretation might lead to important insights into the foundations of fundamental physics.

Subjects: Physics.

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