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On Linearly Kleiman Groups

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Abstract

Let V denote a finite-dimensional vector space over some field. We say that a linear group G ≤ GL(V) is a linearly Kleiman group if, for every pair of linear subspaces v, u ≤ V, there is an element g ∈ G such that the subspaces g(v), u are in general position. The main result of this paper is the classification of connected linear algebraic groups over a field of characteristic zero which are linearly Kleiman. We also consider some properties of linearly Kleiman groups.

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Authors and Affiliations

  1. Department of Mathematics, Russian State Pedagogical University, Moijka 48, St. Petersburg, 191186, Russia

    Nikolai Gordeev

  2. Department of Mathematics, Bielefeled University, Universitätsstrasse 25, D-33615, Bielefeld, Germany

    Ulf Rehmann

Authors
  1. Nikolai Gordeev
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  2. Ulf Rehmann
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Correspondence to Nikolai Gordeev.

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Gordeev, N., Rehmann, U. On Linearly Kleiman Groups. Transformation Groups 18, 685–709 (2013). https://doi.org/10.1007/s00031-013-9230-0

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