Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지

SOME REMARKS ON FOUR KINDS OF POINTS ASSOCIATED TO LIE ALGEBRAS

  • KIM, Y.K. (Dept. of Mathematics, Chonbuk National University) ;
  • SO, K.H. (Dept. of Mathematics, Chonbuk National University) ;
  • SEO, G.S. (Dept. of Mathematics, Chonbuk National University) ;
  • PARK, D.Y. (Dept. of Mathematics, Jeonju University) ;
  • CHOI, S.H. (Dept. of Mathematics, Jeonju University)
  • Received : 1998.01.06
  • Published : 1998.07.30
Download PDF
⟨ Previous Next ⟩

Abstract

Exact definitions of four kinds of points shall be defined associated to Lie algebras L over an algebraically closed field F of prime characteristic p > 0. Next, rough bound of dimensions for L-irreducible modules associated to subregular points shall be established by taking advantage of Premet's result.

Keywords

Acknowledgement

Supported by : Basic Science Research Institute

References

  1. Math. Ann. v.285 Graded Lie algebras with classical reductive null component Benkart, G.;Gregory, T.
  2. Lie algebras(Proceedings) Benkart, G.;Osborn, J.M.
  3. Annals of Math. v.119 Rank one Lie algebras Benkart, G.;Osborn, J.M.
  4. Trans. of the AMS v.318 no.2 Simple Lie algebras of characteristic p with dependent roots Benkart, G.;Osborn, J.M.
  5. Journal of Algebra v.115 Toral rank one Lie algebras Benkart, G.;Osborn, J.M.
  6. J. of Algebra v.114 Classification of the restricted simple Lie algebras Block, R.E.
  7. Annals of Math. v.90 Dertermination of the differentiably simple rings with a minimal ideal Block, R.E.
  8. Annals of Math. v.115 The simple Lie p-algebras of rank two Block, R.E.;Wilson, R.L.
  9. Journal of Math and Mechanics v.9 no.2 Representations of Lie algebras of classical type with applications to linear groups Curtis, C.W.
  10. Algebra Carbondale 1980, Proceedings Dold, A.;Eckmann, B.
  11. Manuscripta Math. v.74 Restricted Lie algebras with bounded cohomology and related classes of algebras Feldvoss, J.;Strade, H.
  12. American J. of Math. v.110 Modular representation theory of Lie algebras Friedlander, E.M.;Parshall, B.J.
  13. Introduction to Lie algebras and Representation theory Humphreys, J.E.
  14. Lie algebras Jacobson, N.
  15. Restricted Lie algebras of characteristic p Jacobson, N.
  16. Abh. Math. Sem. Univ. Hamburg v.56 Kohomologie von p-Lie algebren und nilpotente Elemente Jantzen, J.C.
  17. Honam Mathematical Journal v.15 no.1 An example of subregular germs for $4{\times}4$ symplectic groups Kim, Y.
  18. Journal of the Korean Math. Society v.28 no.2 On whole regular germs for p-adic $Sp_4$(F) Kim, Y.
  19. Can. J. Math. v.XLI Regular germs for p-adic $Sp_4$(F) Kim, Y.
  20. Survey of recent development in Lie algebras and their representation theory Kim, Y.
  21. Bulletin of the Honam Math. Society Witt algebras W( 1 : 1 ) as $sl_2$-modules Kim, Y.;Seo, G.
  22. Bulletin of Korean Math. Soc. v.32 no.2 Some decomposition of modular $sp_4$(F)-modules using dimension formula Kim, Y.;Seo, G.;Won, S.
  23. Comm. Korean Math. Soc. v.7 no.1 What are Chevalley Groups for $sl_2$(F)-module $V(m){\bigotimes}_FV(n)$? Kim, Y.;Won, S.
  24. Honam Mathematical Journal v.19 no.1 On subregular points form some cases of Lie algebra Kim, Y.;So, K.;Seo, G.;Park, D.;Choi, S.
  25. Some criteria for irreducibility of modular $sp_4$(F)-modules Koh, S.H.
  26. Journal of the London Mathematical Society v.55 Support varieties of nonrestricted modules over Lie algebras of reductive groups Premet, A.
  27. Zeitschrift Support varieties of nonrestricted modules over Lie algebras of reductive grou-ps : corrigenda and addenda Premet, A.
  28. Journal of Algebra v.152 Universal Graded Lie algebras Qingyun, F.
  29. Subregular points for some cases of Lie algebras Repka, J.;Kim, Y.
  30. Math. Notes Acad. Sci. USSR v.2 Irreducible representations of a simple three dimensional Lie algebra over a field of finite characteristic Rudakov, A.N.;Shafarevich, I.R.
  31. Journal of Algebra v.11 Cartan decompositions for Lie algebras of prime characteristic Schue, J.R.
  32. Journal of Math. and Mechanics v.6 no.4 Some remarks on classical Lie algebras Seligman, G.B.
  33. Lie algebras and Lie Groups Serre, J.P.
  34. International Journal of Math. and Math. Sciences Some subregular germs for p-adic $Sp_4$(F) So, K.;Kim, Y.
  35. Math. USSR Sbornik v.71 no.1 New methods for the classification of the simple modular Lie algebras Strade, H.
  36. Canadian Journal of Math. v.43 no.3 Representations of the ($p^2-1$)-dimensional Lie Algebras of R.E.BLOCK Strade, H.
  37. Trans. of AMS v.319 no.2 Lie algebra representations of dimension < $p^2$ Strade, H.
  38. Annals of Math. v.130 The classification of the simple modular Lie algebras: I. Determination of the two sections Strade, H.
  39. Journal of Algebra v.151 no.2 The classification of the simple modular Lie algebras II. The toral sturcture Strade, H.
  40. Annals of Math. v.133 The classification of the simple modular Lie algebras: III. Solution of the classical case Strade, H.
  41. Annals of Math. v.138 The classification of the simple modular Lie algebras: IV. Determining the associated graded algebra Strade, H.
  42. Contemporary Mathematics v.110 The role of p-envelopes in the theory of modular Lie algebras Strade, H.
  43. Modular Lie algebras Strade, H.;Farnsteiner, R.
  44. Journal of Algebra v.53 On the structure of the minimal ideal of some graded Lie algebras in characteristic p > 0 Weisfeiler, B.
  45. Journal of Algebra v.40 A structural characterization of the simple Lie algebras of generalized Cartan type over fields of prime characteristic Wilson, R.L.
  46. Trans. of the AMS v.236 Simple Lie algebras of toral rank one Wilson, R.L.
  47. Generalization of [$M_{max}\;:\;M_{min}$] for tensor products Won, S.
  48. Proceedings of Glasgow Math. Assoc. no.2 The representations of Lie algebras of prime characteristic Zassenhaus, H.