Sixteen-dimensional compact translation planes with automorphism groups of dimension at least 35

DOI10.1515/advgeom-2022-0022zbMath1504.51010OpenAlexW4388470372MaRDI QIDQ2087448

Harald Löwe

Publication date: 21 October 2022

Published in: Advances in Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/advgeom-2022-0022

zbMATH Keywords

classificationlarge automorphism groupscompact spreadtopological translation plane

Mathematics Subject Classification ID

Topological linear incidence structures (51H10)

Cites Work

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• S\(U_ 4({\mathbb{C}})\) als Kollineationsgruppe in sechzehndimensionalen lokalkompakten Translationsebenen. \((SU_ 4({\mathbb{C}})\) as collineation group in sixteen-dimensional locally compact translation planes)
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• Automorphismengruppen achtdimensionaler lokalkompakter Quasikörper
• On the kernel and the nuclei of 8-dimensional locally compact quasifields
• Zur Klassifikation von 8- und 16-dimensionalen lokalkompakten Translationsebenen nach ihren Kollineationsgruppen
• Sixteen-dimensional locally compact translation planes with large automorphism groups having no fixed points
• Sixteen-dimensional locally compact translation planes admitting \(\text{SL}_2\mathbb H\) as a group of collinea\-tions.
• Sixteen-dimensional locally compact planes of Lenz-type V on which \(\mathrm{SU}_2\mathbb{H}\) acts as a group of collineations
• Parabolic and unipotent collineation groups of locally compact connected translation planes
• Sechzehndimensionale lokalkompakte Translationsebenen, deren Kollineationsgruppe \(G_ 2\) enthält. (On sixteen-dimensional locally compact translation planes with collineation group containing \(G_ 2)\)
• Near-homogeneous 16-dimensional planes
• Sixteen-dimensional locally compact translation planes with collineation groups of dimension at least 38
• 16-dimensional compact projective planes with 3 fixed points
• Noncompact subgroups of the reduced stabilizer of a locally compact, connected translation plane
• Sixteen-dimensional locally compact translation planes admitting \(SU_4\mathbb{C}\cdot S\mathbb{U}_2\mathbb{C}\) or \(SU_4\mathbb{C}\cdot S\mathbb{L}_2\mathbb{R}\) as a group of collineations

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