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The subalgebra lattice of a supersolvable lie algebra

Part of the Lecture Notes in Mathematics book series (LNM,volume 1373)

1980 Mathematics Subject Classification

  • 17B50

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References

  1. Amayo, R. K.: Quasi-ideals of Lie algebras, Proc. London Math. Soc.33 (1976), 28–36.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Amayo, R. K., Schwarz, J.: Modularity in Lie algebras, Hiroshima Math. J. 10 (1980),311–322.

    MathSciNet  MATH  Google Scholar 

  3. Barnes, D. W.: On Cartan subalgebras of Lie algebras, Math. Z. 101 (1967), 350–355.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Barnes, D. W.: Lattice isomorphisms of Lie algebras, J. Austral. Math. Soc. 4 (1964), 470–475.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Barnes, D. W.: Lattice automorphisms of semisimple Lie algebras, J. Austral. Math. Soc. 16 (1973), 43–45.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Benkart, G. M., Isaacs, I. M., Osborn, J. M.: Lie algebras with self-centralizing adnilpotent elements. J. Algebra 57 (1979), 279–309.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Benkart, G. M., Osborn, J. M.: Rank one Lie algebras. Annals of Math. 119 (1984), 437–463.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Gein, A.G.: Semimodular Lie algebras, Sibirsk. Mat. Z. 17 (1976), 243–248 (translated in Siberian Math. J. 17 (1976), 243–248.

    MathSciNet  MATH  Google Scholar 

  9. Gein, A. G.: Supersolvable Lie algebras and the Dedekind law in the lattice of subalgebras. Ural. Gos. Univ. Mat. Zap. 10 (1977), 33–42.

    MathSciNet  MATH  Google Scholar 

  10. Gein, A.G.: Modular subalgebras and projections of locally finite dimensional Lie algebras of characteristic zero, Ural. Gos. Univ. Mat. Zap. 13 (1983), 39–51.

    MathSciNet  Google Scholar 

  11. Gein, A. G., Muhin, Complements to subalgebras of Lie algebras, Ural. Gos. Univ. Mat. Zap. 12 (1980), 2, 24–48.

    MathSciNet  Google Scholar 

  12. Goto, M.: Lattices of subalgebras of real Lie algebras, J. Algebra 11 (1969), 6–24.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. Jacobson, N.: Lie Algebras, Wiley-Interscience, New York (1962).

    MATH  Google Scholar 

  14. Kolman, B.: Semi-modular Lie algebras, J. Sci. Hiroshima Univ. Ser. A-1 29 (1965), 149–163.

    MathSciNet  MATH  Google Scholar 

  15. Kolman, B.: Relatively Complemented Lie algebras, J. Sci. Hiroshima Univ. Ser. A-1 31 (1967), 1–11.

    MathSciNet  MATH  Google Scholar 

  16. Lashi, A. A.: On Lie algebras with modular lattices of subalgebras, J. Algebra 99 (1986), 80–88.

    CrossRef  MathSciNet  Google Scholar 

  17. Premet, A. A.: Toroidal Cartan subalgebras of Lie p-algebras, and anisotropic Lie algebras of positive characteristic, Vestsi Akad. Navuk BSSR Ser. Fiz. Mat. Navuk, 1 (1986), 9–14.

    MathSciNet  MATH  Google Scholar 

  18. Premet, A.A.: Lie algebras without strong degeneration, Math. USSR Sb. 57 (1987), 151–163.

    CrossRef  MATH  Google Scholar 

  19. Towers, D. A.: Lattice isomorphisms of Lie algebras, Math. Proc. Phil. Soc. 89 (1981), 285–292; corrigenda, 95, (1984), 511–512.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. Towers, D. A.: Lattice automorphisms of Lie algebras, Arch. Math. 46 (1986), 39–43.

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. Towers, D. A.: Semi-modular subalgebras of a Lie algebra, J. Algebra 103 (1986), 202–207.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. Varea, V. R.: Lie algebras whose maximal subalgebras are modular, Proc. of the Royal Soc. of Edinburgh, 94 A (1983), 9–13.

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. Varea, V. R.: Lie algebras none of whose Engel subalgebras are in intermediate position, Comm. in Algebra, 15 (12), (1987), 2529–2543.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1989 Springer-Verlag

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Varea, V.R. (1989). The subalgebra lattice of a supersolvable lie algebra. In: Benkart, G., Osborn, J.M. (eds) Lie Algebras, Madison 1987. Lecture Notes in Mathematics, vol 1373. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088889

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  • DOI: https://doi.org/10.1007/BFb0088889

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