Journal of Lie Theory
8(1), 83-93 (1998)

Large automorphism groups of 16-dimensional planes are Lie groups

B. Priwitzer, H. Salzmann

Mathematisches Institut
Auf der Morgenstelle 10
D -- 72076 Tübingen, Germany

Abstract: It is a major problem in topological geometry to describe all compact projective planes $\scriptstyle\cP$ with an automorphism group $\scriptstyle\Sigma$ of sufficiently large topological dimension. This is greatly facilitated if the group is known to be a Lie group. Slightly improving a result from the first author's dissertation, we show for a 16-dimensional plane $\scriptstyle\cP$ that the connected component of $\scriptstyle\Sigma$ is a Lie group if its dimension is at least 27.

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