On the hyperbolic unitary geometry
Kristina Altmann
and Ralf Gramlich
DOI: 10.1007/s10801-009-0200-5
Abstract
Hans Cuypers (Preprint) describes a characterisation of the geometry on singular points and hyperbolic lines of a finite unitary space-the hyperbolic unitary geometry-using information about the planes. In the present article we describe an alternative local characterisation based on Cuypers' work and on a local recognition of the graph of hyperbolic lines with perpendicularity as adjacency. This paper can be viewed as the unitary analogue of the second author's article (J. Comb. Theory Ser. A 105:97-110, 2004) on the hyperbolic symplectic geometry.
Pages: 547–583
Keywords: keywords hyperbolic unitary geometry; root group geometry; local recognition graphs; centralisers of involutions
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References
1. Altmann, K., Gramlich, R.: Local recognition of the line graph of an anisotropic vector space. Adv. Geom. doi:
2. Bennett, C.D., Shpectorov, S.: A new proof of Phan's theorem. J. Group Theory 7, 287-310 (2004)
3. Cohen, A., Cuypers, H., Gramlich, R.: Local recognition of non-incident point-hyperplane graphs.
2. Bennett, C.D., Shpectorov, S.: A new proof of Phan's theorem. J. Group Theory 7, 287-310 (2004)
3. Cohen, A., Cuypers, H., Gramlich, R.: Local recognition of non-incident point-hyperplane graphs.
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