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Homomorphisms from linear groups over division rings to algebraic groups

Part of the Lecture Notes in Mathematics book series (LNM,volume 1185)

Keywords

  • Algebraic Group
  • Simple Root
  • Parabolic Subgroup
  • Maximal Torus
  • Dynkin Diagram

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References

  1. A. Borel, Linear Algebraic Groups. notes by H.Bass. New York, W.A.Benjania 1969.

    Google Scholar 

  2. A. Borel, T.A. Springer, Rationality properties of linear algebraic groups II. Tohoku Math. J. 20. 443–497. (1968).

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. A. Borel, J. Tits, Homomorphismes "abstraits" de groups algébriques simples. Ann. of Math. 97. 499–571 (1973).

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. A. Borel, J. Tits, Groupes réductifs. Inst. Hautes Etudes Sci. Publ. Math. 27. 55–150 (1960).

    CrossRef  MATH  Google Scholar 

  5. A. Borel, J. Tits, Compléments à l'article "Groupes réductifs". Inst. Hautes Etudes Sci. Publ. Math. 41, 253–276 (1972).

    CrossRef  MATH  Google Scholar 

  6. N.Bourbaki, Groupes et algébres de Lie. Paris, Hermann ch 4–6. 1968.

    Google Scholar 

  7. C.Chevalley, Séminaire sur la classification des groups de Lie algebriques. Paris, Ecole Norm. Sup 1956–1958.

    Google Scholar 

  8. J. Dieudonné, La géométrie des groupes classiques. 3rd ed. Berlin-Heidellberg-Nes York, Springer 1971.

    MATH  Google Scholar 

  9. L.K. Hua, Z.X. Wan, Classical groups, Science and Technomogy press (In Chinese), Schanghai 1963.

    Google Scholar 

  10. D. James, W. Waterhouse, B. Weisfeiler, Abstract homomorphisms of algebraic groups: problems and bibliography. Comm. in Algebra, 9 (1), 95–144 (1981).

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. S.X. Liu, Rings and Algebras. (In Chinese) Science Press. Beijing 1983.

    Google Scholar 

  12. D.Mumford, Introduction to algebraic geometry. Harvard notes.

    Google Scholar 

  13. O. Schreier & B.L. van der Waerden, Die Automorphismen der Projektiven Gruppen. Abh. Math. Sem. Univer. Hamber. 6(1928). 303–322.

    CrossRef  MATH  Google Scholar 

  14. R. Steinberg, Abstract homomorphisms of simple algebraic groups. Sem. Bourbaki (1972–1973) Exp 435. Lect. Notes in Math. 383. Berlin-Heidelberg-New York, Springer 1974.

    Google Scholar 

  15. R.Steinberg, Lecture on Chevalley Groups. mimeographed lecture notes. New Haven, Yale Univ. Math. Dept. 1968.

    Google Scholar 

  16. J. Tits, Classification of algebraic semisimple groups. Procedings of symposia in pure Math. Vol. IX. Amer. Math. Soc. 1966.

    Google Scholar 

  17. B.Weisfeiler, Abstract homomorphisms between subgroups of algebraic groups. Notre Dame University Lecture Notes Series (1982).

    Google Scholar 

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© 1986 Springer-Verlag

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Chen, Y. (1986). Homomorphisms from linear groups over division rings to algebraic groups. In: Tuan, HF. (eds) Group Theory, Beijing 1984. Lecture Notes in Mathematics, vol 1185. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076177

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  • DOI: https://doi.org/10.1007/BFb0076177

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16456-2

  • Online ISBN: 978-3-540-39793-9

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