Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ON SUBREGULAR POINTS FOR SOME CASES OF LIE ALGEBRA

  • 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, Chonju University) ;
  • CHOI, S.H. (Dept. of Mathematics, Chonju University)
  • Received : 1997.01.09
  • Published : 19970000
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Abstract

We shall define three kinds of points for algebraic varieties associated to the center 3 of U(L) which is the universal enveloping algebra of a finite-dimensional modular Lie algebra over an algebraically closed field F of prime characteristic p. We announce here that $sp_4$(F) with p = 2 has a subregular point.

Keywords

Acknowledgement

Supported by : Basic Science Research Institute

References

  1. Math. Ann. v.285 Graded Lie algebras with classical reductive null component G. Benkart;T. Gregory
  2. Lie algebras(Proceedings) G. Benkart;J.M. Osborn
  3. Annals of Math. v.118 Rank one Lie algebras G. Benkart;J.M. Osborn
  4. Trans. of the AMS v.318 no.2 Simple Lie algebras of characteristic p with dependent roots G. Benkart;J.M. Osborn
  5. Annals of Math. v.119 Toral rank one Lie algebras G. Benkart;J.M. Osborn
  6. J. of Algebra v.114 Classification of the restricted simple Lie algebras R.E. Block
  7. Annals of Math. v.90 Determination of the differentiably simple rings with a minimal ideal G. Benkart;J.M. Osborn
  8. Annals of Math. v.115 The simple Lie p-algebras of rank two R.E. Block;R.L. Wilson
  9. Journal of Math and Mechanics v.9 no.2 Representations of Lie algebras of classical type with applications to linear groups C.W. Curtis
  10. Proceedings Algebra Carbondale 1980 A. Dold;B. Eckmann
  11. Manuscripta Math. v.74 Restricted Lie algebras with bounded cohomology and related classes of algebras J. Feldvoss;H. Strade
  12. American J. of Math. v.110 Modular representation theory of Lie algebras E.M. Friedlander;B.J. Parshall
  13. Introduction of Lie algebras and Representation theory J.E. humphreys
  14. Lie algebras N. Jacobson
  15. Restricted Lie algebras of characteristic p N. Jacobson
  16. Honam Mathematical Journal v.15 no.1 An example of subregular germs for 4 × 4 symplectic groups Y. Kim
  17. Journal of the Korean Math. Society v.28 no.2 On whole regular germs for p-adic Sp₄(F) Y. Kim
  18. Can. J. Math. XLI Regular germs for p-adic Sp₄(F) Y. Kim
  19. Survey of recent development in Lie algebras and their representation theory Y. Kim
  20. Bulletin of the Honam Math. Society Witt algebras W(1 : 1) as sl₂-modules Y. Kim;G. Seo
  21. Bulletin of Korean Math. Soc. v.32 no.2 Some decomposition of modular sp₄(F)-modules using dimension formula Y. Kim;G. Seo;S. Won
  22. Comm. Korean Math. Soc. v.7 no.1 What are Chevalley Groups for sl₂(F)-module V(m)ⓧ$_FV$(n)? Y. Kim;S. Won
  23. Journal of Math. and Mechanics v.6 Lie algebras of classical type W.H. Mills;G.B. Seligman
  24. Journal of Algebra v.152 Universal Graded Lie algebras F. Qingyun
  25. Subregular points for some cases of Lie algebras J. Repka;Y. Kim
  26. Math. Notes Acad. Sci. USSR v.2 Irreducible representations of a simple three dimensional Lie algebra over a field of finite characteristic A.N. Rudakov;I.R. Shafarevich
  27. Journal of Algebra v.11 Cartan decompositions for Lie algebras of prime characteristic J.R. Schue
  28. Journal of Math. and Mechanics v.6 no.4 Some remarks on classical Lie algebras G.B. Seligman
  29. Lie algebras and Lie Groups J.P. Serre
  30. International Journal of Math. and Math. Sciences Some subregular germs for p-adic Sp₄(F) K. So;Y. Kim
  31. Math. USSR Sbornik v.71 no.1 New methods for the classificatin of the simple modular Lie algebras H. Strade
  32. Canadian Journal of Math. v.43 no.3 Representations of the (p²-1)-dimensional Lie Algebras of R.E.BLOCK H. Strade
  33. Trans. of AMS v.319 no.2 Lie algebra representations of dimension < p² H. Strade
  34. Annals of Math. v.130 The classification of the simple modular Lie algebras: Ⅰ. Determination of the two sections H. Strade
  35. Journal of Algebra v.151 no.2 The classification of the simple modular Lie algebras: Ⅱ. The toral structure H. Strade
  36. Annals of Math. v.133 The classification of the simple modular Lie algebras: Ⅲ. Solution of the classical case H. Strade
  37. Annals of Math. v.138 The classification of the simple modular Lie algebras: Ⅳ. Determining the associated graded algebra H. Strade
  38. Contemporary Mathematics v.110 The role of p-envelopes in the theory of modular Lie algebras H. Strade
  39. Modular Lie algebras H. Strade;R. Farnsteiner
  40. Journal of Algebra v.53 On the structure of the minimal ideal of some graded Lie algebras in characteristic p > 0 B. Weisfeiler
  41. Journal of Algebra v.40 A structural characterization of the simple Lie algebras of generalized Cartan type over fields of prime characteristic R.L. Wilson
  42. Trans. of the AMS v.236 Lie algebras of toral rank one R.L. Wilson
  43. Ph.d dissertation, Chonbug National Univ. Generalization of [$M_{max}$ : $M_{min}$] for tensor products S. Won
  44. Proceedings of Glasgow Math. Assoc. no.2 The representations of Lie algebras of prime characteristic H. Zassenhaus