Monatshefte für Mathematik

, Volume 123, Issue 3, pp 253–273 | Cite as

The skew-hyperbolic motion group of the quaternion plane

  • Markus Stroppel


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.

1991 Mathematics Subject Classification

51H20 51A10 

Key words

Stable planes eight-dimensional stable planes compact projective planes quaternion planes 


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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Markus Stroppel
    • 1
  1. 1.Mathematisches Institut B/1Universität StuttgartStuttgartGermany

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