A class of simple Lie algebras of characteristic three
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- by Gordon Brown PDF
- Proc. Amer. Math. Soc. 107 (1989), 901-905 Request permission
Abstract:
We show the existence of a certain infinite class of simple Lie algebras of characteristic three. These algebras, although of neither classical nor Cartan type, resemble algebras of Cartan type in their relationship to each other.References
- Richard E. Block and Robert Lee Wilson, Classification of the restricted simple Lie algebras, J. Algebra 114 (1988), no. 1, 115–259. MR 931904, DOI 10.1016/0021-8693(88)90216-5
- Gordon Brown, Properties of a $29$-dimensional simple Lie algebra of characteristic three, Math. Ann. 261 (1982), no. 4, 487–492. MR 682662, DOI 10.1007/BF01457452
- Gordon Brown, Freudenthal triple systems of characteristic three, Algebras Groups Geom. 1 (1984), no. 4, 399–441. MR 785425
- John R. Faulkner, A construction of Lie algebras from a class of ternary algebras, Trans. Amer. Math. Soc. 155 (1971), 397–408. MR 294424, DOI 10.1090/S0002-9947-1971-0294424-X
- Marguerite Frank, A new simple Lie algebra of characteristic three, Proc. Amer. Math. Soc. 38 (1973), 43–46. MR 314924, DOI 10.1090/S0002-9939-1973-0314924-0
- A. I. Kostrikin, A parametric family of simple Lie algebras, Izv. Akad. Nauk SSSR Ser. Mat. 34 (1970), 744–756 (Russian). MR 0274539
- Robert Lee Wilson, Classification of generalized Witt algebras over algebraically closed fields, Trans. Amer. Math. Soc. 153 (1971), 191–210. MR 316523, DOI 10.1090/S0002-9947-1971-0316523-6
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 107 (1989), 901-905
- MSC: Primary 17B50; Secondary 17B20
- DOI: https://doi.org/10.1090/S0002-9939-1989-0993742-6
- MathSciNet review: 993742