Hermann Hähl

Sixteen-Dimensional Locally Compact Translation Planes with Large Automorphism Groups having no Fixed Points

The 16-dimensional compact projective planes whose automorphism group contains a closed connected subgroup fixing a line, but no point and having dimension at least 35 are determined. It is shown that these planes all belong to three families of planes determined by H. Löwe and the author, and hence are explicitly known. A major stepping stone to this goal is a result by H. Salzmann according to which every such plane is a translation plane.