Large semisimple groups on 16-dimensional compact projective planes are almost simple

The paper deals with the so-called Salzmann program aiming to classify special geometries according to their automorphism groups. Here, topological connected compact projective planes are considered. If finite-dimensional, such planes are of dimension 2, 4, 8, or 16. The classical example of a 16-dimensional, compact projective plane is the projective plane over the octonions with 78-dimensional automorphism group E-6(-26). A 16-dimensional, compact projective plane P admitting an automorphism group of dimension 41 or more is classical, [18] 87.5 and 87.7. For the special case of a semisimple group Delta acting on P the same result can be obtained if dim Delta greater than or equal to 37, see [16]. Our aim is to lower this bound. We show: if Delta is semisimple and dim Delta greater than or equal to 29, then P is either classical or a Moufang-Hughes plane or Delta is isomorphic to Spin(9) (IR, r), r is an element of {0,1}. The underlying paper contains the first part of the proof showing that Delta is in fact almost simple.