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Geometries and Groups pp 467–480Cite as

The 2-spaces of the standard E 6(q)-module

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Abstract

Let 픽 be a field and let 핂 be the vector space of dimension 27 over 픽 whose elements are the triples x = [x 1, x 2, x 3] with x i ∈ M 3(픽), the set of 3 × 3-matrices with entries in 픽, for i = 1,2,3, with addition and scalar multiplication taken entrywise.

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References

  1. Aschbacher, M., The 27-dimensional module for E 6 , preprint (1987).

    Google Scholar 

  2. Chevalley, C., Sur le groupe exceptionnel (E 6 ), Comptes Rendues de I’ Acad. Franc. Paris 232 (1951) 1991–1993.

    MathSciNet  MATH  Google Scholar 

  3. Cohen, A.M. and B.N. Cooperstein, A characterization of some geometries of exceptional Lie type, Geometriae Dedicata 15 (1983) 73–105.

    Article  MathSciNet  MATH  Google Scholar 

  4. Cooperstein, B.N., A characterization of some Lie incidence structures, Geometriae Dedicata 6 (1977) 205–258.

    Article  MathSciNet  MATH  Google Scholar 

  5. Dickson, L., A class of groups in the arbitrary realm connected with the configuration of the 27 lines on a cubic surface, Quarterly J. Pure Appl. Math. 33 (1901) 145–173.

    Google Scholar 

  6. Freudenthal, H Beziehungen der E 7 und E 8 Oktavenebene, I, Indagationes Math. (1954) 218–230.

    Google Scholar 

  7. Jacobson, N., Some groups of transformations defined by Jordan algebras III, J. f.d. reine u. angew. Math. 207 (1961) 61–85.

    Article  MATH  Google Scholar 

  8. Jacobson, N., Structure Theory of Jordan Algebras, Lecture Notes in Math., Vol. 5, University of Arkansas, Fayetteville. (1981).

    Google Scholar 

  9. Mars, J.G.M., Les nombres de Tamagawa de certains groupes exceptionnels, Bull, de la Société Math, de France 94 (1966) 97–140.

    MathSciNet  MATH  Google Scholar 

  10. Springer, T.A., Characterization of a class of cubic forms, Indagationes Math. 24 (1962) 259–265.

    MathSciNet  Google Scholar 

  11. Springer, T.A.,Linear Algebraic Groups, Progress in Math., Vol. 9, Birkhäuser, Basel (1981).

    Google Scholar 

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Author information

Authors and Affiliations

  1. CWI, Kruislaan 413, 1098, SJ Amsterdam, The Netherlands

    Arjeh M. Cohen

  2. University of California at Santa Cruz, 95064, Santa Cruz, CA, USA

    Bruce N. Cooperstein

Authors
  1. Arjeh M. Cohen
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  2. Bruce N. Cooperstein
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Editor information

Editors and Affiliations

  1. CalTech, Pasadena, USA

    M. Aschbacher

  2. CWI, Amsterdam, The Netherlands

    A. M. Cohen

  3. IAS, Princeton, USA

    W. M. Kantor

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© 1988 D. Reidel Publishing Company, Dordrecht, Holland

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Cohen, A.M., Cooperstein, B.N. (1988). The 2-spaces of the standard E 6(q)-module. In: Aschbacher, M., Cohen, A.M., Kantor, W.M. (eds) Geometries and Groups. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4017-8_16

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  • DOI: https://doi.org/10.1007/978-94-009-4017-8_16

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8282-2

  • Online ISBN: 978-94-009-4017-8

  • eBook Packages: Springer Book Archive

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