Groups of compact 8-dimensional planes: conditions implying the Lie property (Q2331934)

Let \(\Sigma\) be the automorphism group of a compact topological projective plane with an \(8\)-dimensional point space; compare [the author et al., Compact projective planes. With an introduction to octonion geometry. Berlin: de Gruyter (1996; Zbl 0851.51003)]. If \(\dim \Sigma \ge 12\), then the locally compact group \(\Sigma\) is even a (real) Lie group by \textit{B. Priwitzer} [Geom. Dedicata 52, No. 1, 33--40 (1994; Zbl 0810.51003)]. This result is extended in the paper under review: the connected component \(\Sigma^1\) of \(\Sigma\) is a Lie group if \(\dim \Sigma^1 \ge 10\), provided that \(\Sigma^1\) is semisimple or does not fix just an anti-flag or a double-flag.