Abstract
We mentioned previously (cf. Chapter II) that the fundamental problem of geometry is to set up an isomorphism of an abstractly given geometry with the geometry of subspaces of a vector space. In this chapter we shall examine this problem. The classical result in this direction asserts that for a geometry of dimension ≥ 4 there exists always an isomorphism with the projective geometry of a vector space, and that such an isomorphism can be constructed even when the dimension is 3, provided the geometry is what is known as Desarguesian. These are of course well known results.
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© 1968 Springer Science+Business Media New York
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Varadarajan, V.S. (1968). Coordinatization of Generalized Geometries. In: Geometry of Quantum Theory. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-7706-5_5
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DOI: https://doi.org/10.1007/978-1-4615-7706-5_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4615-7708-9
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