Quasifields of symplectic translation planes |
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Authors: | N Knarr |
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Institution: | Institute of Geometry and Topology, University of Stuttgart, 70550 Stuttgart, Germany |
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Abstract: | We show that a translation plane is symplectic if and only at least one of its associated quasifields admits a non-degenerate invariant symmetric bilinear form. As an application we prove that a proper desarguesian, Moufang or nearfield plane can never be symplectic. Moreover, we give a purely algebraic characterization of the quasifields which coordinatize symplectic translation planes. |
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Keywords: | Symplectic spread Quasifield Invariant bilinear form Kernel Nuclei |
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