Journal of Lie Theory, Vol. 9, No. 2, pp. 481-486 (1999)

Large automorphism groups of 16-dimensional planes are Lie groups, II

Helmut Salzmann

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

Abstract: Let $\cal{P}$ be a compact, 16-dimensional projective plane. If the group $\Sigma$ of all continuous collineations of $\cal{P}$ is taken with the compact-open topology, then $\Sigma$ is a locally compact group with a countable basis. The following theorem is proved: Theorem. If the topological dimension $\dim \Sigma$ is at least 29, then $\Sigma$ is a Lie group. [Part I appeared in Vol. 8, No. 1, pp. 83-93 (1998).]

Keywords: 16-dimensional projective planes, continuous collineations, locally compact groups, topological dimension, Lie groups

Classification (MSC91): 51H10; 57S20

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