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Generation of Lie Incidence Geometries: A Survey

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Groups of Exceptional Type, Coxeter Groups and Related Geometries

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 82))

Abstract

A subspace of a point-line geometry \((\mathcal{P}, \mathcal{L})\) is a subset \(S\) of the point set \(\mathcal{P}\) with the property that whenever a line \(L\) meets \(S\) in at least two points then \(L\) is contained in \(S\). For an arbitrary subset \(X\) of \(\mathcal{P}\) the subspace generated by \(X\), denoted by \(\langle X \rangle _\varGamma \), is the intersection of all subspaces which contain \(X\). A subset \(X\) is said to generate \(\varGamma \) if \(\langle X \rangle _\varGamma = \mathcal{P}\). The generating rank of \(\varGamma \) is the minimal cardinality of a generating set. In this paper we survey what is currently know about the generating rank of the Lie incidence geometries arising as the shadow of a spherical building.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Santa Cruz, U.S.A.

    Bruce N. Cooperstein

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  1. Bruce N. Cooperstein
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Correspondence to Bruce N. Cooperstein .

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Editors and Affiliations

  1. Stat Math Unit, Indian Statistical Institute, Bangalore, Karnataka, India

    N.S. Narasimha Sastry

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Cooperstein, B.N. (2014). Generation of Lie Incidence Geometries: A Survey. In: Sastry, N. (eds) Groups of Exceptional Type, Coxeter Groups and Related Geometries. Springer Proceedings in Mathematics & Statistics, vol 82. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1814-2_5

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