Abstract
For a rank two incidence system\((\mathcal{P}, \mathcal{L})\) and a projective embedding\(e:(\mathcal{P}, \mathcal{L}) \to \mathbb{P}\mathbb{G}(V)\) the concepts ofe- indepedence of a point set and a basis of\((\mathcal{P}, \mathcal{L})\) are defined. It is then demonstrated that for a Lie incidence geometry\((\mathcal{P}, \mathcal{L})\) of type Bn,n and Cn,1 over a field of characteristic not two, An,k,Dn,1,Dn,n,E6,1 or E7,1,\(Aut(\mathcal{P}, \mathcal{L})\) is transitive on certain classes of subsets called frames. As a consequence we obtain a characterization of the apartments of these geometries and demonstrate that the frames are bases.
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This work supported in part by an National Security Agency grant
This work supported in part by an National Science Foundation grant
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Cooperstein, B.N., Shult, E.E. Frames and bases of Lie incidence geometries. J Geom 60, 17–46 (1997). https://doi.org/10.1007/BF01252215
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DOI: https://doi.org/10.1007/BF01252215