Affine polar spaces derived from polar spaces and Grassmann structures defined on them

2012/08/21 by Krzysztof Prażmowski, K. Prażmowski, Prażmowski, K. +3
Mathematics · #51A10 #51A50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Metric Geometry (math.MG) #math.CO #math.MG #msc:51A10 #msc:51A50

paper · pdf · doi:10.48550/arxiv.1208.4387

arxiv created 2012/08/21 · openalex publication_date 2012/08/21 · arxiv updated 2012/08/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We prove that an affine polar space in the meaning of Cohen and Shult can be recovered from one of the three adjacency relations on a Grassmann structure over it. The result directly generalizes the results of our previous work where we use an affine space over a vector space equipped with a nondegenerate reflexive form as a starting point to the Cohen-Shult affine polar spaces.

Citations

• Causality Implies the Lorentz Group

Related

• Affine polar spaces derived from symplectic spaces, their geometry and representations: alternating semiforms
• An outline of polar spaces: basics and advances
• Transformations of polar Grassmannians preserving certain intersecting relations
• Base subsets of polar Grassmannians
• Opposite relation on dual polar spaces and half-spin Grassmann spaces