Sixteen-dimensional compact translation planes with automorphism groups of dimension at least 35
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Harald Löwe
Abstract
The present paper investigates 16-dimensional compact translation planes with automorphism groups of dimension d between 35 and 37; planes with groups of higher dimensions have been classified by Hähl. We obtain a complete classification for d = 37 (up to isomorphisms). It turns out that these planes have Lenz type V and are already described in a recent paper of Hähl and Meyer [10]. Moreover, we give a partial classification for d = 35 and d = 36. The latter case will be completely finished in a forthcoming paper [16] of the author, while the case where d = 35 is completed except for groups whose maximal compact subgroups are 9-dimensional.
Communicated by: R. Löwen
References
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Articles in the same Issue
- Frontmatter
- On weak Fano manifolds with small contractions obtained by blow-ups of a product of projective spaces
-
A geographical study of
- A characterization of centrally symmetric convex bodies in terms of visual cones
- Closed Majorana representations of {3, 4}+-transposition groups
- Real hypersurfaces in ℂP2 and ℂH2 with constant scalar curvature
- Positive semigroups in lattices and totally real number fields
- A new axiomatics for masures II
- Helmut Salzmann and his legacy
- Some remarks on proper actions, proper metric spaces, and buildings
- Regular parallelisms on PG(3,ℝ) from generalized line stars: the oriented case
- A note on the Kleinewillinghöfer types of 4-dimensional Laguerre planes
- Sixteen-dimensional compact translation planes with automorphism groups of dimension at least 35
