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Classification of simple Lie algebras over algebraically closed fields of prime characteristic


Authors: Helmut Strade and Robert Lee Wilson
Journal: Bull. Amer. Math. Soc. 24 (1991), 357-362
MSC (1985): Primary 17B20
DOI: https://doi.org/10.1090/S0273-0979-1991-16033-7
MathSciNet review: 1071032
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  • Georgia Benkart, Simple modular Lie algebras with 1-sections that are classical or solvable, Comm. Algebra 18 (1990), no. 11, 3633–3638. MR 1068610, https://doi.org/10.1080/00927879008824097
  • Georgia Benkart and Thomas Gregory, Graded Lie algebras with classical reductive null component, Math. Ann. 285 (1989), no. 1, 85–98. MR 1010192, https://doi.org/10.1007/BF01442673
  • [BOSt-pre] G. Benkart, J. M. Osborn, and H. Strade, Contributions to the classification of simple modular Lie algebras (submitted).
  • [Blo-58] R. E. Block, New simple Lie algebras of prime characteristic, Trans. Amer. Math. Soc. 89 (1958), 421-449. MR 100010
  • Richard E. Block and Robert Lee Wilson, Classification of the restricted simple Lie algebras, J. Algebra 114 (1988), no. 1, 115–259. MR 931904, https://doi.org/10.1016/0021-8693(88)90216-5
  • [Dem-70] S. P. Demuškin, Cartan subalgebras of the simple Lie p-algebras W, Sibirsk. Mat. Zk. 11 (1970), 310-325 (Russian); Siberian Math. J. 11 (1970), 233-245. (English transl.) MR 262310
  • [Dem-72] S. P. Demuškin, Cartan subalgebras of simple nonclassical Lie p-algebras, Izv. Akad. Nauk SSSR Ser. Math. 36 (1972), 915-932 (Russian); Math. USSR-Izv. 6 (1972), 905-924. (English transl.) MR 327854
  • [Kac-71] V. G. Kac, Global Cartan pseudogroups and simple Lie algebras of characteristic p, Uspekhi Math. Nauk 26 (1971), 199-200. (Russian) MR 311731
  • [Kac-74] V. G. Kac, Description of filtered Lie algebras with which graded Lie algebras of Cartan type are associated, Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974), 800-834; Errata, 40 (1976), 1415 (Russian); Math. USSR-Izv. 8 (1974), 801-835; Errata, 10 (1976), 1339 (English transl.) MR 369452
  • [Kap-54] I. Kaplansky, Seminar on simple Lie algebras, Bull. Amer. Math. Soc. (N.S.) 60 (1954), 470-471. MR 26643
  • [Kos-70] A. I. Kostrikin, Variations modulaires sur un thème de Cartan, Actes du Congrès International des Mathematiciens (Nice, 1970), Tome 1, Gauthier-Villars, Paris, 1971, pp. 285-292. MR 435166
  • Helmut Strade, The absolute toral rank of a Lie algebra, Lie algebras, Madison 1987, Lecture Notes in Math., vol. 1373, Springer, Berlin, 1989, pp. 1–28. MR 1007321, https://doi.org/10.1007/BFb0088884
  • Helmut Strade, The classification of the simple modular Lie algebras. I. Determination of the two-sections, Ann. of Math. (2) 130 (1989), no. 3, 643–677. MR 1025169, https://doi.org/10.2307/1971457
  • [St-pre-1] H. Strade, The classification of the simple modular Lie algebras: II. The toral structure (submitted).
  • [St-pre-2] H. Strade, New methods for the classification of simple modular Lie algebras, Mat. Sb. (to appear).
  • [St-pre-3] H. Strade, Representations of the (p2 - 1)-dimensional Lie algebras of R. E. Block (submitted).
  • Helmut Strade, The classification of the simple modular Lie algebras. III. Solution of the classical case, Ann. of Math. (2) 133 (1991), no. 3, 577–604. MR 1109354, https://doi.org/10.2307/2944320
  • [St-pre-5] H. Strade, The classification of the simple modular Lie algebras: IV. Solution of Cases C and D, preprint.
  • [StW-pre] H. Strade and R. L. Wilson, The classification of the simple modular Lie algebras: V. Solution of Case A, preprint.
  • [Wei-68] B. Ju. Weisfeiler, Infinite-dimensional filtered Lie algebras and their connection with graded Lie algebras, Funktsional. Anal. i Prilozhen 2 (1968), 94-95. (Russian) MR 232811
  • B. Weisfeiler, On the structure of the minimal ideal of some graded Lie algebras in characteristic 𝑝>0, J. Algebra 53 (1978), no. 2, 344–361. MR 502633, https://doi.org/10.1016/0021-8693(78)90280-6
  • [Wil-76] R. L. Wilson, A structural characterization of the simple Lie algebras of generalized Cartan type over fields of prime characteristic, J. Algebra 40 (1976), 418-465. MR 412239
  • Robert Lee Wilson, Simple Lie algebras over fields of prime characteristic, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986) Amer. Math. Soc., Providence, RI, 1987, pp. 407–416. MR 934240

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DOI: https://doi.org/10.1090/S0273-0979-1991-16033-7

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