Abstract
As main theorem we show that any duality in the projective geometry associated to a vector space is induced by a non-degenerate sesquilinear form on this space. In particular, any polarity is induced by a non-degenerate orthosymmetric sesquilinear form.
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References
Baer, R.: Polarities in finite projective planes,Bull. Amer. Math. Soc. 52 (1946), 77–93.
Baer, R.:Linear Algebra and Projective Geometry, Academic Press, New York, 1952.
Ball, R. W.: Dualities of finite projective planes,Duke Math. J. 15 (1948), 929–940.
Birkhoff, G., and von Neumann, J.: The logic of quantum mechanics,Ann. Math. 37 (1936), 823–843.
Faure, C.-A. and Frölicher, A.: Morphisms of projective geometries and of corresponding lattices,Geom. Dedicata 47 (1993), 25–40.
Faure, C.-A. and Frölicher, A.: Morphisms of projective geometries and semilinear maps,Geom. Dedicata 53 (1994), 237–262.
Gross, H.:Quadratic Forms in Infinite Dimensional Vector Spaces. Birkhäuser, Boston, 1979.
Maeda, F. and Maeda, S.:Theory of Symmetric Lattices, Springer, Berlin, 1970.
Piron, C.:Foundations of Quantum Physics, Benjamin, Massachusetts, 1976.
Piziak, R.: Lattice theory, quadratic spaces, and quantum proposition system,Found. Phys. 20 (1990), 651–665.
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Supported by a grant from the Swiss National Founds for Scientific Research.
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Faure, CA., Frölicher, A. Dualities for infinite-dimensional projective geometries. Geom Dedicata 56, 225–236 (1995). https://doi.org/10.1007/BF01263563
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DOI: https://doi.org/10.1007/BF01263563