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    Three-dimensional connected groups of automorphisms of toroidal circle planes (2018)

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    http://hdl.handle.net/10092/16484
    
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    • Science: Journal Articles [1139]
    Authors
    Creutz B
    Ho D
    Steinke GF
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    Abstract

    We contribute to the classification of toroidal circle planes and flat Minkowski planes possessing three-dimensional connected groups of automorphisms. When such a group is an almost simple Lie group, we show that it is isomorphic to $\text{PSL}(2,\mathbb{R})$. Using this result, we describe a framework for the full classification based on the action of the group on the point set.

    ANZSRC Fields of Research
    49 - Mathematical sciences::4904 - Pure mathematics::490402 - Algebraic and differential geometry

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    • On automorphism groups of toroidal circle planes 

      Creutz B; Ho D; Steinke GF (2018)
      © 2018, Springer International Publishing AG, part of Springer Nature. Schenkel proved that the automorphism group of a flat Minkowski plane is a Lie group of dimension at most 6 and described planes whose automorphism ...
    • A family of 2-dimensional Minkowski planes with small automorphism groups 

      Steinke, Günter F. (University of Canterbury. Dept. of Mathematics, 1994)
      This paper concerns 2-dimensional (topological locally compact connected) Minkowski planes. It uses a construction of J. Jakóbowski [4] of Minkowski planes over half-ordered fields and applies it to the field of reals. ...
    • Projective planes, Laguerre planes and generalized quadrangles that admit large groups of automorphisms 

      Steinke GF (2018)
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