Vol. 17, No. 3, 2019

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Groups of compact 8-dimensional planes: conditions implying the Lie property

Helmut R. Salzmann

Vol. 17 (2019), No. 3, 201–220

The automorphism group Σ of a compact topological projective plane with an 8-dimensional point space is a locally compact group. If the dimension of Σ is at least 12, then Σ is known to be a Lie group. For the connected component Δ of Σ it is shown that dimΔ 10 suffices, if Δ is semisimple or does not fix exactly a nonincident point-line pair or a double-flag. Δ is also a Lie group, if Δ has a compact connected 1-dimensional normal subgroup and dimΔ 11.

topological plane, Lie group
Mathematical Subject Classification 2010
Primary: 22D05, 51H10
Received: 18 November 2018
Revised: 19 March 2019
Accepted: 27 April 2019
Published: 9 October 2019
Helmut R. Salzmann
Mathematisches Institut
Universität Tübingen