Abstract
Up to conjugation, there exist three different polarities of the projective plane ℍ over Hamilton's quaternions ℍ. The skew hyperbolic motion group of P2ℍ is introduced as the centralizer of a polarity “of the third kind”. According to a result of R. Löwen, the quaternion plane is characterized among the eight-dimensional stable planes by the fact that it admits an effective action of the centralizer of a polarity of the first or second kind (i.e., the elliptic or the hyperbolic motion group). In the present paper, we prove the analogous result for skew hyperbolic case.
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Stroppel, M. The skew-hyperbolic motion group of the quaternion plane. Monatshefte für Mathematik 123, 253–273 (1997). https://doi.org/10.1007/BF01318236
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DOI: https://doi.org/10.1007/BF01318236