scholarly journals A characterization of the SDPS-hyperplanes of dual polar spaces

2007 ◽  
Vol 28 (3) ◽  
pp. 705-714 ◽  
Author(s):  
Bart De Bruyn
Keyword(s):  
Polar Spaces ◽  
Dual Polar Spaces

scholarly journals Minimal scattered sets and polarized embeddings of dual polar spaces

2007 ◽  
Vol 28 (7) ◽  
pp. 1890-1909 ◽  
Author(s):  
Bart De Bruyn ◽  
Antonio Pasini
Keyword(s):  
Polar Spaces ◽  
Dual Polar Spaces

scholarly journals Opposite Relation on Dual Polar Spaces and Half-Spin Grassmann Spaces

2009 ◽  
Vol 54 (3-4) ◽  
pp. 301-308 ◽  
Author(s):  
Mariusz Kwiatkowski ◽  
Mark Pankov
Keyword(s):  
Polar Spaces ◽  
Dual Polar Spaces

scholarly journals Non-Classical Hyperplanes of Finite Thick Dual Polar Spaces

10.37236/7348 ◽  
2018 ◽  
Vol 25 (1) ◽  
Author(s):  
Bart De Bruyn
Keyword(s):  
Complete Classification ◽  
Polar Spaces ◽  
Dual Polar Spaces

We obtain a classification of the nonclassical hyperplanes of all finite thick dual polar spaces of rank at least 3 under the assumption that there are no ovoidal and semi-singular hex intersections. In view of the absence of known examples of ovoids and semi-singular hyperplanes in finite thick dual polar spaces of rank 3, the condition on the nonexistence of these hex intersections can be regarded as not very restrictive. As a corollary, we also obtain a classification of the nonclassical hyperplanes of $DW(2n-1,q)$, $q$ even. In particular, we obtain a complete classification of all nonclassical hyperplanes of $DW(2n-1,q)$ if $q \in \{ 8,32 \}$.

scholarly journals Dual polar spaces of arbitrary rank

2011 ◽  
Vol 11 (3) ◽  
Author(s):  
Simon Huggenberger
Keyword(s):  
Polar Spaces ◽  
Arbitrary Rank ◽  
Dual Polar Spaces

scholarly journals Universal and homogeneous embeddings of dual polar spaces of rank 3 defined over quadratic alternative division algebras

2016 ◽  
Vol 2016 (715) ◽  
Author(s):  
Bart De Bruyn ◽  
Hendrik Van Maldeghem
Keyword(s):  
Division Algebra ◽  
Division Algebras ◽  
Polar Spaces ◽  
Dual Polar Spaces

AbstractSuppose 𝕆 is an alternative division algebra that is quadratic over some subfield 𝕂 of its center

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