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On the Cardinality of Finite Tits Geometries

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Beiträge zur Geometrischen Algebra

Part of the book series: Mathematische Reihe ((LMW/MA,volume 21))

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Abstract

An inductive way to compute the number of elements of geometries over a field with q elements, belonging to Lie group graphs,2 will be described. In order to simplify the formulae, the abbreviation

EquationSource% MathType!MTEF!2!1!+- % feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqr % pepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs % 0-yqaqpepae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaai % aabeqaamaabaabauaakeaadaWadaqaaiaadIhaaiaawUfacaGLDbaa % cqGH9aqpcaWGXbWaaWbaaSqabeaacaWG4baaaOGaeyOeI0IaaGymaa % aa!46E7!]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$\left[ x \right] = {q^x} - 1$$

is used. q = 1 is allowed (the geometries of Weyl groups); then expressions like [x y]/[y] will be understood in an obvious way.

Republished from Philips Research Reports 30 (1975), 196-204.

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Reference

  1. Chevalley, C.: Tohoku math. J. (2) 7 14–66 (1955) (in particular, p. 64).

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Authors and Affiliations

  1. Universität Utrecht, Tiberdreef 4, Utrecht, Niederlande

    H. Freudenthal

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  1. H. Freudenthal
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Hans J. Arnold Walter Benz Heinrich Wefelscheid

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© 1977 Springer Basel AG

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Freudenthal, H. (1977). On the Cardinality of Finite Tits Geometries. In: Arnold, H.J., Benz, W., Wefelscheid, H. (eds) Beiträge zur Geometrischen Algebra. Mathematische Reihe, vol 21. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5573-0_13

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  • DOI: https://doi.org/10.1007/978-3-0348-5573-0_13

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5574-7

  • Online ISBN: 978-3-0348-5573-0

  • eBook Packages: Springer Book Archive

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