New flag-transitive geometries for the groups {Mathematical expression} and {Mathematical expression}

Justin F. McInroy; Harm Pralle; Sergey Shpectorov

doi:10.1007/s10711-013-9928-0

New flag-transitive geometries for the groups {Mathematical expression} and {Mathematical expression}

Justin F. McInroy^*, Harm Pralle, Sergey Shpectorov

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In Pralle and Shpectorov (Adv Geom 7(1):1-17, 2007) the class of ovoidal hyperplanes in dual polar spaces of rank 4 is described. In this paper we observe that by removing such a hyperplane and a related second hyperplane one obtains a nice geometry for the group stabilising the ovoidal hyperplane. We show that this group acts flag-transitively and that the geometry is simply connected.

Original language	English
Pages (from-to)	65–82
Number of pages	18
Journal	Geometriae Dedicata
Volume	173
Issue number	1
Early online date	25 Oct 2013
DOIs	https://doi.org/10.1007/s10711-013-9928-0
Publication status	Published - Dec 2014

Keywords

Affine
Biaffine
Flag-transitive
Geometry
Hyperplane
Polar space
Simply connected

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s10711-013-9928-0

Cite this

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title = "New flag-transitive geometries for the groups {Mathematical expression} and {Mathematical expression}",

abstract = "In Pralle and Shpectorov (Adv Geom 7(1):1-17, 2007) the class of ovoidal hyperplanes in dual polar spaces of rank 4 is described. In this paper we observe that by removing such a hyperplane and a related second hyperplane one obtains a nice geometry for the group stabilising the ovoidal hyperplane. We show that this group acts flag-transitively and that the geometry is simply connected.",

keywords = "Affine, Biaffine, Flag-transitive, Geometry, Hyperplane, Polar space, Simply connected",

author = "McInroy, {Justin F.} and Harm Pralle and Sergey Shpectorov",

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T1 - New flag-transitive geometries for the groups {Mathematical expression} and {Mathematical expression}

AU - McInroy, Justin F.

AU - Pralle, Harm

AU - Shpectorov, Sergey

PY - 2014/12

Y1 - 2014/12

N2 - In Pralle and Shpectorov (Adv Geom 7(1):1-17, 2007) the class of ovoidal hyperplanes in dual polar spaces of rank 4 is described. In this paper we observe that by removing such a hyperplane and a related second hyperplane one obtains a nice geometry for the group stabilising the ovoidal hyperplane. We show that this group acts flag-transitively and that the geometry is simply connected.

AB - In Pralle and Shpectorov (Adv Geom 7(1):1-17, 2007) the class of ovoidal hyperplanes in dual polar spaces of rank 4 is described. In this paper we observe that by removing such a hyperplane and a related second hyperplane one obtains a nice geometry for the group stabilising the ovoidal hyperplane. We show that this group acts flag-transitively and that the geometry is simply connected.

KW - Affine

KW - Biaffine

KW - Flag-transitive

KW - Geometry

KW - Hyperplane

KW - Polar space

KW - Simply connected

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U2 - 10.1007/s10711-013-9928-0

DO - 10.1007/s10711-013-9928-0

M3 - Article

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EP - 82

JO - Geometriae Dedicata

JF - Geometriae Dedicata

IS - 1

ER -

New flag-transitive geometries for the groups {Mathematical expression} and {Mathematical expression}

Abstract

Keywords

ASJC Scopus subject areas

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